Holographic Recording Materials (Topics in Applied Physics) 354008293X, 9783540082934

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Topics in Applied Physics Volume 20

Topics in Applied Physics

Founded by Helmut K. V. Lotsch

Volume

1

Dye Lasers

Volume

2

Laser Spectroscopy of Atoms and Molecules Editor: H. Walther

Volume

3

Numerical and Asymptotic Editor: R. Mittra

2nd Edition

Editor : F. P. Schafer

Techniques in Electromagnetics

Volume 4

Interactions on Metal Surfaces

Editor:

Volume

5

Miissbauer Spectroscopy

Volume

6

Picture Processing and Digital Filtering

Volume

7

Integrated Optics

R. Gomer

Editor: U. Gonser Editor: T. S. Huang

Editor: T. Tamir

Volume 8

Light Scattering in Solids

Editor:

M. Cardona

Volume

9

Laser Speckle and Related Phenomena

Volume

10 Transient Electromagnetic

Fields

Volume

11 Digital Picture Analysis

Editor: A. Rosenfeld

Volume

12 Turbulence

Editor: J. C. Dainty

Editor: L,. B. Felsen

Editor: P. Bradshaw

Volume

High-Resolution

Laser Spectroscopy

Editor:

K. Shimoda

Volume

Laser Monitoring

of the Atmosphere

Volume

Radiationless Processes in Molecules and Condensed Phases Editor: F. K. Fong

Volume

Nonlinear Infrared Generation

Volume

Electroluminescence

Volume

Ultrashort Light Pulses. Picosecond Techniques and Editor: S. L. Shapiro Applications

Editor: E. D. Hinkley

Editor: Y.-R. Shen

Editor: J. I. Pankove

Volume

19 Optical and Infrared Detectors

Volume

20 Holographic Recording Materials

Volume

21 Solid Electrolytes

Volume

22 X-Ray Optics. Applications Editor: H.-J. Queisser

Volume

23 optical

Volume

24 Acoustic Surface Waves

Editor: R. J. Keyes Editor: H. M. Smith

Editor: S. Geller to Solids

Data Processing. Application.,

Editor: D. Casasent

Editor: A. A. Oliner

Holographic Recording Materials Edited by H. M. Smith With Contributions by R. A. Bartolini K. Biedermann J. Bordogna R. C. Duncan, Jr. S.A. Keneman D. Meyerhofer H. M. Smith D . L . Staebler J.C. Urbach

With 96 Figures

Springer-Verlag Berlin Heidelberg New York 1977

Howard M. Smith, Ph. D. Eastman Kodak Company, 343 State Street Rochester, NY 14650, USA

ISBN 3-540-08293-X Springer-Verlag Berlin Heidelberg New York ISBN 0-387-08293-X Springer-Verlag New York Heidelberg Berlin Library of Congress Cataloging in Publication Data. Main entry under title: Holographic recording materials. (Topics in applied physics; v. 20). Includes bibliographical references and index. I. Holography-Equipment and supplies. 1. Smith, Howard Michael, 1938-. II. Bartolini, Robert A. TA 1542.H 64 621.36 77-24503 This work is subject to copyright. All rights are reserved, whether the whole or part of Ihe material is concerned, specifically those of translation, reprinting, re-use of illustrations, hroadcasting, reproduction by photocopying mnchine or simdar means, and storage in data banks. Under § 54 of the German Copyrighl Law, where copies are made for olhcr Ihan privale use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. (~) by Springer-Verlag Berlin Heidelberg 1977 Printed in Germany The use of registered names, trademarks, etc. in this publicatic, n does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free general use Monopholo lypesetliug, offset printing, and bookbinding: Briihlsche Universitiitsdi uckerei, I,ahn-Gief]en 2 53/3130/543210

Preface

With most new or advancing technologies, the period of discovery and initial investigation of fundamental principles is immediately followed by a period of intensive search for materials. This is the period when potential applications are being explored and engineering and design begin. The recent discoveries of the transistor and the laser are two prime examples of this type of technological evolution. A third example is the invention and recent renaissance of holography. Following the revival in 1962 to 1964 there came a prolonged (and indeed, ongoing) search for an ideal recording material. The purpose of this volume is to present the up-to-date results of this search. The timing is right for a book devoted solely to recording materials, not only because so much work has been done, but also because the science and engineering of holography have done a good deal of "settling-in". The needs, aims, and applications have become well defined and the range of useful applications has been narrowed to the extent that whether or not a particular application is viable may well depend on the availability of a suitable recording material. These reasons, and also the fact that, in most cases, each different holographic application has its own unique requirement for a recording material, point up the need for a book on the subject of recording materials. It is the aim of this volume to satisfy this need. The basic theory and principles of holography have been covered in a summary fashion in the introductory chapter. The purpose here is simply to acquaint the reader with the basic theory and terminology so that the ensuing chapters can be devoted totally to describing recording materials. I have tried to ensure that every known holographic (or laser) recording material is covered. The authors have ensured that each chapter represents the present state-of-the-art, even to the extent that some material is presented here for the first time. The book is intended to be a monograph, but with so many individual contributors there is bound to be some overlap and inconsistency of notation in spite of the best efforts of the editor. For these I apologize, but I would hope that their effect will be minor and in no way detract from the content of each chapter. Rochester, New York June, 1977

H. M. Smith

Contents

1.

Basic Holographic Principles. By H. M. Smith (With 7 Figures) 1.1 1.2 1.3 1.4

History . . . . . . . . . . . . . . . . . Basic D e s c r i p t i o n . . . . . . . . . . . . Classification . . . . . . . . . . . . . . D i f f r a c t i o n Efficiency . . . . . . . . . . . 1.4.1 Plane H o l o g r a m s . . . . . . . . . . Amplitude Holograms . . . . . . . . Phase H o l o g r a m s . . . . . . . . . . 1.4.2 V o l u m e H o l o g r a m s . . . . . . . . . C o u p l e d Wave T h e o r y . . . . . . . . Transmission Holograms . . . . . . . Reflection H o l o g r a m s . . . . . . . . Summary . . . . . . . . . . . . . 1.5 Noise . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . .

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1 2 3 5 6 6 9 10 10 13 16 17 18 19

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21

2. Silver Halide Photographic Materials. By K. B i e d e r m a n n (With 25 Figures)

2.1 T h e H o l o g r a p h i c Process . . . . . . . . . . . . . . . . . 2.2 T h e Silver H a l i d e E m u l s i o n . . . . . . . . . . . . . . . . 2.3 T h e Practical P r o c e d u r e o f M a k i n g H o l o g r a m s a n d Spatial Filters 2.3.1 P h o t o g r a p h i c M a t e r i a l s A v a i l a b l e . . . . . . . . . . . 2.3.2 R e c o r d i n g a H o l o g r a m . . . . . . . . . . . . . . . Aspects o n Material, Size, and G e o m e t r y . . . . . . . . A D e v i a t i o n on A n t i r e f l e c t i o n T r e a t m e n t . . . . . . . . M o r e o n C h o o s i n g Material, Size, a n d G e o m e t r y .... Intensity Ratio K and Exposure . . . . . . . . . . . . 2.3.3 Processing . . . . . . . . . . . . . . . . . . . . . Standard Procedures . . . . . . . . . . . . . . . . Special Developers . . . . . . . . . . . . . . . . . 2.3.4 R e c o n s t r u c t i o n . . . . . . . . . . . . . . . . . . . 2.3.5 Real T i m e I n t e r f e r o m e t e r with in Situ D e v e l o p m e n t 2.4 Characteristic P a r a m e t e r s o f T h i n A m p l i t u d e H o l o g r a m s a n d Their E v a l u a t i o n . . . . . . . . . . . . . . . . . . . . . 2.4.1 The T w o - S t e p T r a n s f e r Process . . . . . . . . . . . .

22 22 25 25 26 26 26 26 27 28 28 31 31 32 34 34

VIII

Contents

2.4.2 T h e M a c r o s c o p i c C h a r a c t e r i s t i c . . . . . . . . . . . . 2.4.3 T h e M i c r o s c o p i c C h a r a c t e r i s t i c . . . . . . . . . . . . The Modulation Transfer Function (MTF) . . . . . . . T h e M T F in C o h e r e n t L i g h t . . . . . . . . . . . . . M e t h o d s for M e a s u r i n g M T F at H i g h Spatial F r e q u e n c i e s The Microdensitometer . . . . . . . . . . . . . . . . The Diffraction Method . . . . . . . . . . . . . . . The Multiple-Sine-Slit Microdensitometer . . . . . . . . M o d u l a t i o n T r a n s f e r D a t a o f Silver H a l i d e M a t e r i a l s 2.4.4 S c a t t e r e d F l u x S p e c t r u m . . . . . . . . . . . . . . . 2.4.5 F i g u r e o f M e r i t a n d A t t e m p t s to I m p r o v e P h o t o g r a p h i c Materials . . . . . . . . . . . . . . . . . . . . . H o l o g r a p h i c E x p o s u r e Index . . . . . . . . . . . . . W a y s o f I n c r e a s i n g the H o l o g r a p h i c E x p o s u r e I n d e x E x t e n d i n g Sensitivity to I n f r a r e d R a d i a t i o n . . . . . . . 2.4.6 H o l o g r a p h y vs. P h o t o g r a p h y . . . . . . . . . . . . . 2.5 Effects . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 M a c r o s c o p i c N o n l i n e a r T r a n s f e r . . . . . . . . . . . 2.5.2 M i c r o s c o p i c N o n l i n e a r T r a n s f e r . . . . . . . . . . . 2.5.3 C o m p l e x G r a t i n g F o r m a t i o n . . . . . . . . . . . . . 2.5.4 " E m u l s i o n S t r e s s " . . . . . . . . . . . . . . . . . 2.6 E x p e r i m e n t a l D a t a on D i f f r a c t i o n Efficiency a n d S i g n a l - t o - B a c k ground Ratio of Thin Amplitude Holograms . . . . . . . . . 2.7 P h a s e H o l o g r a m s . . . . . . . . . . . . . . . . . . . . 2.7.1 Principles o f Phase G r a t i n g G e n e r a t i o n . . . . . . . . 2.7.2 B l e a c h i n g P r o c e d u r e s . . . . . . . . . . . . . . . . Gelatine Relief Formation . . . . . . . . . . . . . . Bleaching . . . . . . . . . . . . . . . . . . . . . G a s e o u s Bleaching . . . . . . . . . . . . . . . . . R e v e r s a l Processes . . . . . . . . . . . . . . . . . 2.7.3 E x p e r i m e n t a l D a t a on D i f f r a c t i o n Efficiency a n d S i g n a l - t o Background Ratio . . . . . . . . . . . . . . . . . 2.8 T h i c k H o l o g r a m s . . . . . . . . . . . . . . . . . . . . 2.8.1 C h a r a c t e r i s t i c s o f T h i c k P h o t o g r a p h i c E m u l s i o n s .... 2.8.2 M a t e r i a l s A v a i l a b l e ; P r o b l e m s . . . . . . . . . . . . 2.8.3 H o l o g r a m s o f E x t e n d e d T h i c k n e s s . . . . . . . . . . . 2.8.4 E x p e r i m e n t a l D a t a on D i f f r a c t i o n Efficiency a n d S i g n a l - t o Background Ratio of Thick Holograms . . . . . . . . 2.9 S u m m a r y . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . .

3. D i c h r o m a t e d Gelatin. By D. M e y e r h o f e r ( W i t h 5 F i g u r e s ) ..... 3.1 Basic P h o t o c h e m i s t r y . . . . . . . . . . . . . . . . . . . 3.1.1 D i c h r o m a t e d C o l l o i d L a y e r s . . . . . . . . . . . . .

34 36 36 37 38 38 39 41 43 44 48 48 49 49 50 50 51 53 55 56 57 59 59 61 61 62 63 64 64 66 66 67 68 68 70 71

75 76 76

Contents 3.1.2 T h e Properties of G e l a t i n . . . . . . . . . . . . . . 3.1.3 P h o t o s e n s i t i v i t y o f the D i c h r o m a t e I o n . . . . . . . . . 3.2 D i c h r o m a t e d G e l a t i n as a P h o t o s e n s i t i v e M e d i u m . . . . . . 3.2.1 D i c h r o m a t e d G e l a t i n as a Photoresist . . . . . . . . . 3.2.2 P h o t o c h e m i s t r y o f P r e h a r d e n e d D i c h r o m a t e d G e l a t i n Layers 3.2.3 The S h a n k o f f T e c h n i q u e o f Phase Shift E n h a n c e m e n t 3.2.4 V a r i a t i o n in E m u l s i o n T h i c k n e s s D u r i n g Processing . . 3.3 P r e p a r a t i o n a n d Processing o f H a r d e n e d D i c h r o m a t e d G e l a t i n Plates for T h i c k H o l o g r a m s . . . . . . . . . . . . . . . . 3.3.1 P r e p a r a t i o n o f Plates . . . . . . . . . . . . . . . . 3.3.2 D e v e l o p m e n t P r o c e d u r e . . . . . . . . . . . . . . . 3.3.3 Stability o f D i c h r o m a t e d G e l a t i n H o l o g r a m s . . . . . . 3.4 H o l o g r a p h i c Properties o f H a r d e n e d D i c h r o m a t e d G e l a t i n . . . 3.4.1 Phase Shift A v a i l a b l e . . . . . . . . . . . . . . . . 3.4.2 Sensitivity . . . . . . . . . . . . . . . . . . . . . 3.4.3 R e s o l u t i o n . . . . . . . . . . . . . . . . . . . . . 3.4.4 I m a g e Q u a l i t y a n d Noise . . . . . . . . . . . . . . . 3.4.5 Storage C a p a c i t y . . . . . . . . . . . . . . . . . . 3.5 A p p l i c a t i o n s . . . . . . . . . . . . . . . . . . . . . . 3.5.1 H o l o g r a p h i c Optical E l e m e n t s . . . . . . . . . . . . 3.5.2 D u p l i c a t e H o l o g r a m s in D i c h r o m a t e d G e l a t i n ..... References . . . . . . . . . . . . . . . . . . . . . . . . . 4. Ferroelectric Crystals. By D. L. Staebler (With 13 Figures)

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4.1 T h e o r y of M e c h a n i s m s . . . . . . . . . . . . . . . . 4.1.1 Storage . . . . . . . . . . . . . . . . . . . . 4.1.2 E r a s u r e . . . . . . . . . . . . . . . . . . . . 4.1.3 Fixing . . . . . . . . . . . . . . . . . . . . . 4.1.4 Electrical E n h a n c e m e n t . . . . . . . . . . . . . 4.2 Materials a n d P r e p a r a t i o n . . . . . . . . . . . . . . . 4.2.1 L i t h i u m N i o b a t e (LiNbO3) . . . . . . . . . . . . 4.2.2 S t r o n t i u m B a r i u m N i o b a t e (SBN) . . . . . . . . . 4.2.3 B a r i u m T i t a n a t e (BaTiO3) . . . . . . . . . . . . 4.2.4 B a r i u m S o d i u m N i o b a t e . . . . . . . . . . . . . 4.2.5 L i t h i u m T a n t a l a t e (LiTaO3) . . . . . . . . . . . 4.2.6 P o t a s s i u m T a n t a l a t e N i o b a t e ( K T N ) . . . . . . . . 4.2.7 P L Z T C e r a m i c s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 M e t h o d s o f Use 4.3.1 R e a d / W r i t e . . . . . . . . . . . . . . . . . . 4.3.2 R e a d / W r i t e with N o n d e s t r u c t i v e R e a d o u t ( N D R O ) 4.3.3 R e a d - O n l y . . . . . . . . . . . . . . . . . . . 4.3.4 M u l t i p h o t o n A b s o r p t i o n . . . . . . . . . . . . . 4.3.5 Layered M e m o r y . . . . . . . . . . . . . . . . 4.3.6 H o l o g r a p h i c Page Synthesis . . . . . . . . . . .

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IX 77 78 79 79 80 82 85 87 87 89 91 91 91 93 95 95 96 97 97 98 98 101 102 102 108 109 114 115 115 117 118 118 118 118 119 ! 19 120 120 121 121 122 123

X

Contents

4.4 H o l o g r a p h i c P r o p e r t i e s . . . . . . . . . . . . . . . . . . 4.4.1 S e n s i t i v i t y . . . . . . . . . . . . . . . . . . . . . 4.4.2 D y n a m i c R a n g e . . . . . . . . . . . . . . . . . . 4.4.3 R e s o l u t i o n . . . . . . . . . . . . . . . . . . . . . 4.4.4 S t o r a g e T i m e . . . . . . . . . . . . . . . . . . . . 4.4.5 N o i s e a n d D i s t o r t i o n . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . .

123 123 126 128 128 129 130

5. Inorganic Photochromic Materials. By R. C. Duncan, Jr. a n d D. L. S t a e b l e r ( W i t h 20 F i g u r e s )

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5.1 Basic M o d e l . . . . . . . . . . . . . . . . . . . . . . . 5.2 P h o t o c h r o m i c C a F 2, S r T i O 3 , C a T i O 3 . . . . . . . . . . . . 5.2.1 O p t i m u m D o p a n t s a n d C o n c e n t r a t i o n s . . . . . . . . 5.2.2 P h o t o c h r o m i c A b s o r p t i o n S p e c t r a . . . . . . . . . . . 5.2.3 O p t i c a l R e c o r d i n g M o d e s . . . . . . . . . . . . . . 5.2.4 O p t i c a l R e a d o u t at 514.5 n m . . . . . . . . . . . . . Thickness Effects . . . . . . . . . . . . . . . . . . Contrast Ratio . . . . . . . . . . . . . . . . . . . 5.2.5 E r a s e M o d e S e n s i t i v i t y at 514.5 n m . . . . . . . . . . 5.2.6 S e n s i t o m e t r i c C h a r a c t e r i s t i c s a n d T i m e - I n t e n s i t y R e c i procity . . . . . . . . . . . . . . . . . . . . . . C a F z : L a , N a a n d C a F 2 : Ce, N a . . . . . . . . . . . S r T i O 3 : N i , M o , A1 a n d C a T i O 3 : N i , M o . . . . . . . . 5.3 H o l o g r a m S t o r a g e . . . . . . . . . . . . . . . . . . . . 5.3.1 S e n s i t i v i t y . . . . . . . . . . . . . . . . . . . . . 5.3.2 M a x i m u m E f f i c i e n c y . . . . . . . . . . . . . . . . 5.3.3 S t o r a g e C a p a c i t y . . . . . . . . . . . . . . . . . . 5.4 P h o t o d i c h r o i c s . . . . . . . . . . . . . . . . . . . . . 5.4.1 M o d e l . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 H o l o g r a m S t o r a g e . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . .

133 134 135 135 136 139 140 140 141 141 145 146 148 151 152 154 155 156 156 158 159

6. Thermoplastic Hologram Recording. By J. C. U r b a c h ( W i t h 14 F i g u r e s )

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6.1 P r o c e s s D e s c r i p t i o n . . . . . . . . . . . . . . . . . . . 6.1.1 T h e r m o p l a s t i c E l e c t r o n B e a m R e c o r d i n g . . . . . . . . 6.1.2 P h o t o s e n s i t i v e R e c o r d i n g . . . . . . . . . . . . . . Photoplastic Devices . . . . . . . . . . . . . . . . Thermoplastic-Overcoated Photoconductor Devices . . Device and Process Variations . . . . . . . . . . . . 6.1.3 P r o c e s s M o d e l s a n d T h e o r i e s . . . . . . . . . . . . . Theories of Random Deformation . . . . . . . . . . . 6.1.4 M a t e r i a l s . . . . . . . . . . . . . . . . . . . . . .

161 161 162 163 164 166 167 168 170 171

Contents Substrates a n d C o n d u c t i v e C o a t i n g s . . . . . . . . . Photoconductors . . . . . . . . . . . . . . . . . Special P h o t o c o n d u c t o r s . . . . . . . . . . . . . . Thermoplastic Materials . . . . . . . . . . . . . . 6.1.5 F a b r i c a t i o n T e c h n i q u e s . . . . . . . . . . . . . . Substrates a n d C o n d u c t i v e C o a t i n g s . . . . . . . . . Photoconductor Fabrication . . . . . . . . . . . . Thermoplastic Fabrication . . . . . . . . . . . . . Overcoating and Matrixing . . . . . . . . . . . . . 6.2 H o l o g r a p h i c Properties . . . . . . . . . . . . . . . . . 6.2.1 B a n d w i d t h a n d R e s o l u t i o n . . . . . . . . . . . . . 6.2.2 Sensitivity a n d D i f f r a c t i o n Efficiency . . . . . . . . D i f f r a c t i o n Efficiency C o n s i d e r a t i o n s . . . . . . . . E x p e r i m e n t a l E x p o s u r e R e s p o n s e Results . . . . . . 6.2.3 Noise . . . . . . . . . . . . . . . . . . . . . . E x p e r i m e n t a l Noise M e a s u r e m e n t s . . . . . . . . . 6.2.4 Cyclic O p e r a t i o n . . . . . . . . . . . . . . . . . 6.2.5 O t h e r Physical Properties . . . . . . . . . . . . . Shelf Life . . . . . . . . . . . . . . . . . . . . L a t e n t I m a g e Life . . . . . . . . . . . . . . . . . A r c h i v a l Life . . . . . . . . . . . . . . . . . . . M e c h a n i c a l D u r a b i l i t y and C o n t a m i n a t i o n . . . . . . 6.3 C o n c l u s i o n s . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . .

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XI 171 172 176 177 181 181 182 184 185 186 186 191 192 194 197 199 201 202 202 203 203 204 205 206

7. Photoresists. By R. A. Bartolini (With 11 Figures) . . . . . . . . . 7.1 Types o f Photoresists . . . . . . . . . . . . . . . . . . . 7.2 T h e o r y o f M e c h a n i s m . . . . . . . . . . . . . . . . . . 7.3 H o l o g r a m N o n l i n e a r i t i e s . . . . . . . . . . . . . . . . . 7.4 D i f f r a c t i o n Efficiency a n d S i g n a l - t o - N o i s e R a t i o . . . . . . . 7.5 Shipley A Z - 1 3 5 0 Photoresist Characteristics . . . . . . . . . 7.5.1 Shipley A Z - 1 3 5 0 M a t e r i a l N o n l i n e a r i t y C o n s i d e r a t i o n s . 7.5.2 Shipley A Z - 1 3 5 0 R e s o l u t i o n C a p a b i l i t y . . . . . . . . 7.5.3 Shipley AZ-1350 Relief Phase H o l o g r a m Design P r o c e d u r e References . . . . . . . . . . . . . . . . . . . . . . . . .

221 226

8. O t h e r Materials and Devices. By J. B o r d o g n a a n d S. A. K e n e m a n (With l F i g u r e ) . . . . . . . . . . . . . . . . . . . . . . .

229

8.1 M a g n e t o - O p t i c F i l m s . . . . . . . . . . . . 8.2 Metal F i l m s . . . . . . . . . . . . . . . . 8.3 Layered Devices with P h o t o c o n d u c t o r W r i t e - I n 8.3.1 F e r r o e l e c t r i c - P h o t o c o n d u c t o r Devices . 8.3.2 L i q u i d - C r y s t a l - P h o t o c o n d u c t o r Devices 8.3.3 P h o t o c o n d u c t o r - P o c k e l ' s Effect Devices

. . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . .

209 211 211 213 215 217 218 220

. .

230 231

. . . .

232 232 235 236

Xll

Contents 8.3.4 E l a s t o m e r D e v i c e s . . . . . . . . . . . . . . . . . 8.3.5 A d v a n t a g e s a n d L i m i t a t i o n s o f P h o t o c o n d u c t o r - B a s e d Devices . . . . . . . . . . . . . . . . . . . . . . 8.4 C h a l c o g e n i d e Glasses . . . . . . . . . . . . . . . . . . . 8.4.1 M a t e r i a l s E x h i b i t i n g an A m o r p h o u s - C r y s t a l l i n e Ph ase Change . . . . . . . . . . . . . . . . . . . . . . . 8.4.2 AszS 3 a n d R e l a t e d M a t e r i a l s . . . . . . . . . . . . . 8.4.3 P h o t o d o p i n g D e v i c e s . . . . . . . . . . . . . . . . 8.4.4 S u m m a r y . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . .

A d d i t i o n a l R e f e r e n c e s with T i t l e s

. . . . . . . . . . . . . . . . .

237 238 238 239 239 241 241 241

245

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . .

247

Subject Index

249

. . . . . . . . . . . . . . . . . . . . . . . . .

Contributors

Bartolini, Robert A. RCA Laboratories, David Sarnoff Research Center, Princeton, NJ 08540, USA Biedermann, Klaus The Royal Institute of Technology, Dept. of Physics and Institute of Optical Research, S-10044 Stockholm, Sweden Bordogna, Joseph Moore School of Electrical Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA Duncan, Robert C., Jr. RCA Laboratories, David Sarnoff Research Center, Princeton, NJ 08540, USA Keneman, Scott A. RCA Laboratories, David Sarnoff Research Center, Princeton, NJ 08540, USA Meyerhofer, Dietrich RCA Laboratories, David Sarnoff Research Center, Princeton, NJ 08540, USA Smith, Howard M. Research Laboratories, Eastman Kodak Company, 343 State Street, Rochester, NY 14650, USA Staebler, David L. RCA Laboratories, David Sarnoff Research Center, Princeton, NJ 08540, USA Urbach, John C. Palo Alto Research Center, Xerox Corp., Palo Alto, CA 94304, USA

1. Basic Holographic Principles H. M. Smith With 7 Figures

With most new or advancing technologies, the period of discovery and initial investigation of fundamental principles is immediately followed by a period of intensive search for materials. The recent discoveries of the transistor and laser are two prime examples of this type of technological evolution. A third example is the invention and recent renaissance of holography. Following the revival in 1962-64, there came a prolonged (and indeed, ongoing) search for an ideal recording material. The purpose of this monograph is to present the results of this search. 1.1

History

The history of holography begins with its invention by Gabor [1.1] in 1948. His ideas and demonstrations form the foundation of modern holography. Because of the severe limitations imposed by having to work with a totally inadequate light source, among other reasons, few practical uses were found for holography, even though it represented a fundamentally different method of image formation. However, in the period 1962-64 Leith and Upatnieks [1.2, 3] published a series of papers describing methods for overcoming two of the major problems associated with the earlier techniquesIthe limited coherence and intensity of the light and the very problematical mixing of the signal (image forming) and illuminating waves during readout. These papers created a great deal of excitement and the whole field of holography underwent a rebirth. The coherence problem was solved by the invention of the laser. Its use as a source for holography allowed for the diffuse illumination of large, three-dimensional objects and thus the ability to view the reconstruction, complete with parallax and depth effects, with the unaided eye. The use of the laser also permitted great latitude and flexibility in the choice of object to be used and of the physical layout of the recording setup--a degree of freedom undreamed of by the early workers in the 1950's [1.4-11]. The second problem, that o f the mixing o f the signal and illuminating waves, was solved by Leith and Upatnieks by the use of an off-axis (noncollinear) reference beam to record the hologram. This allowed reconstruction with a similarly off-axis illuminating beam. Since this light was traveling in a substantially different direction, it no longer obscured the image-forming light.

2

H . M . Smith

By this simple technique they were able to solve one of the major problems with the earlier forms of holography. At about the same time, D e n i s y u k [1.12] in Russia and Van H e e r d e n [1.13] in the USA were expanding the basic 1948 concepts to include the recording of waves that could be reconstructed by reflection of white light and waves that could be recorded throughout a large volume of the recording material. As a result ofall of the aforementioned innovations, new life was given to the old idea of holography. Not only was its practicality well demonstrated, but the striking three-dimensional images that could be produced fired the imaginations of many thousands of students and scientists throughout the world. The vast amount of activity in the field during the time span of roughly 1964 through 1970 resulted in many new ideas for application, creating a demand for increasingly better recording materials, a demand that in large part has been satisfied.

1.2 Basic Description If O represents a monochromatic wave from the object, and R a reference wave coherent with O, the total field at the recording medium is O + R so that a squarelaw recording medium responds to the irradiance IO + R] 2. After processing, the hologram recording material has a certain complex amplitude transmittance Ta(x) that can be expressed as a function of the exposure E(x) = t[O + R[ 2 (t is the exposure time): T,(x) = fiE(x) = fitlO + RI 2 = fit([OI 2 + ]RI 2 + OR* + O ' R ) ,

(1.1)

where the * denotes complex conjugate and/3 depends on the recording material involved. When the hologram with this amplitude transmittance is illuminated with a wave C, the transmitted wave at the hologram is ~(x) = CZ(x) = flt(ClO[ 2 + CIR] 2 + C R * O + C R O * ) .

(1.2)

If the illuminating wave C is sufficiently uniform so that C R * is approximately constant across the hologram, the third term of (1.2) becomes simply a constant x O. Thus this term represents a reconstructed wave that is identical to the original object wave O. The other terms represent the zero-order wave fiCt(J01 z +IRI 2) and the other first-order wave f i C t R O * . The latter is known as the "conjugate" wave. These terms represent the waves that caused the problems referred to above with the early G a b o r holograms. But because of the offset reference beam associated with this type of hologram, these waves are spatially separated from the desired reconstruction wave. Tiffs is the main advantage of the off-axis technique and is the principal reason for the resurgence of interest in holography in 1964.

Basic HolographicPrinciples

3

1.3 Classification Holograms are classified as to type with the recording geometry, the type of modulation imposed on the illuminating wave, the thickness of the recording material, and the mode of image formation as factors. If the two interfering beams are traveling in substantially the same direction, the recording of the interference pattern is said to be a Gabor hologram or an inline hologram. If the two interfering beams arrive at the recording medium from substantially different directions, the recording is a Leith-Upatnieks or off-axis hologram. If the two interfering beams are traveling in essentially opposite directions, the recorded hologram is said to be a Lippmann or reflection hologram. These hologram types are further classified, depending on recording geometry, as Fresnel, Fourier Transform, Fraunhofer, or Lensless Fourier Transform. Generally speaking, if the object is reasonably close to the recording medium, say 10 or so hologram or object diameters distant, the field at the hologram plane is the Fresnel diffraction pattern of the object, and the hologram thus recorded is a Fresnel hologram. If, on the other hand, the object and recording medium are separated by many hologram or object diameters, the field at the recording plane is the Fraunhofer or far field diffraction pattern of the object and a Fraunhofer hologram results. Ifa lens is used to produce the far field pattern at the recording plane, with the lens a focal length distant from both the object and recording plane, then a Fourier Transform hologram results, provided the reference wave is plane. Lastly, if the reference beam originates from a point that is the same distance from the recording plane as the object, then a so-called Lensless Fourier Transform hologram results. Any of the foregoing hologram types may also be recorded as a thick or thin hologram. A thin (or plane) hologram is one for which the thickness of the recording medium is small compared to the fringe spacing. A thick (or volume) hologram is one for which the thickness is of the order of or greater than the fringe spacing. The distinction between thick and thin holograms is usually made with the aid of the Q-parameter defined as

Q =-2rtXd/(nAZ),

(1.3)

where 2 is the illuminating wavelength, n the index of the recording material, d its thickness, and A the spacing of the recorded fringes. The hologram is considered thick when Q > 10 and thin otherwise, although it has recently been shown [1.14] that thick hologram theory (coupled wave theory) is quite accurate even for Q values of order 1. Finally, holograms are also classified by the mechanism by which the illuminating light is diffracted. In an amplitude hologram the interference pattern is recorded as a density variation of the recording medium, and the amplitude of the illuminating wave is accordingly modulated. In a phase hologram, a phase modulation is imposed on the illuminating wave.

4

H.M. Smith

The amplitude transmittance of a hologram is a complex function that describes the change in the amplitude and phase of an illuminating wave upon transmission through the material. If the illuminating field is described by the complex function C(x)=Co(x)exp[iq)o(X)] and the transmitted field by lp(x) = bz(x)exp [i~0t(x)] then the amplitude transmittance of the hologram is defined as the ratio of these two quantities: T a ( x ) = lp(x) __

[bt]

LCoJ

ei(O _~oo)

(1.4)

In most instances, the illuminating wave C is constant or nearly so, so that the complex amplitude transmittance is given by T~(x)= b,(x)eie'(x) .

(1.5)

If bt(x ) is not constant but qot(x) is, it is the amplitude of the illuminating wave that is modulated and the hologram is an amplitude hologram. The magnitude of bt(x ) depends on the absorption constant a and the thickness of the recording material according to b,(x) = Co(x)e - ,,(x)e.

(1.6)

Thus for an amplitude hologram the transmitted amplitude is modulated in accordance with the exposure, since the exposure causes a spatial variation of the absorption constant a. The two most common recording materials that can accomplish this are silver halide photographic emulsions (Chap. 2) and photochromic materials (Chap. 5). If, on the other hand, b,(x) is constant and ~o,(x) varies, then the phase of the illuminating wave is modulated and the hologram is a phase hologram. The phase of the illuminating wave can be modulated in one or both of two different ways. Ifa surface relief is found as the result of exposure to the interference fringe pattern, then the thickness of the material is a function of x. If the index of refraction of the material is changed in accordance with the exposure, then the optical path of the transmitted light is a function ofx. In either case, the phase of the transmitted light will vary with x because the optical path nd will be a function ofx. The phase rp, of the transmitted light is related to the optical path according to 27~

(p, = --~- nd .

(1.7)

A phase hologram results when q~, is a function of the exposure--such as when either the index of refraction n or the thickness d, or both, is exposure dependent. From (1.7) it is seen that a change A~0, in q~r is given by 27~

Aq), = ~ - [ d A n + ( n -

1)Ad],

(1.8)

Basic Holographic Principles

5

where the n - 1 factor appears assuming the hologram to be in air. If the hologram is thin, d is very small and the contribution to A~0, from the term dAn is negligible and

Acp, = 2~ ( n - 1)Ad.

(1.9)

This would be a surface relief hologram, achieved mainly by embossing, etching a photo resist material, or with a thermoplastic film (Chap. 3). For a thick hologram, on the other hand, having a negligible surface relief but a varying index, we have 2~

Aq~t = ~ - dAn.

(1.10)

Typical materials for this type of hologram are bleached photographic emulsions (Chap. 2), dichromated gelatin (Chap. 3), and ferroelectric crystals (Chap. 4). All of these materials (and others) are discussed in detail in the following chapters.

1.4 Diffraction Efficiency Diffraction efficiency is defined as the ratio of the total, useful, image-forming light flux diffracted by the hologram to the total light flux used to illuminate the hologram. If some of the illuminating light is diffracted into an unwanted .conjugate (or primary) image, it is still only the light in the primary (or conjugate) image that is pertinent to the stated diffraction efficiency. The importance of producing a hologram with a reasonable diffraction efficiency is obvious, whether the application is simply the viewing of a three-dimensional scene, holographic interferometry, or data storage; efficient use of the illuminating light allows for smaller and more economical systems. Being able to use a smaller and cheaper laser for illumination or readout, for example, could be the deciding factor in determining the feasibility of a holographic data storage system. However, one must approach the question of diffraction efficiency with some careful thought. In many cases it is the output signal-to-noise ratio (s/n) that is the more important consideration. The noise in a holographic image arises principally from three factors: intrinsic nonlinearity, such as in phase holograms, that causes unwanted light to be diffracted into the image region ; the nonlinearity of the amplitude transmittance-exposure characteristic of the recording medium ; and the noise caused by the buildup of the granular structure of the recording material. (A discussion of the sources of noise in holographic images follows in Sect. 5.) It is, however, possible to increase the diffraction efficiency without seriously impairing the s/n characteristics o f the recording by a judicious choice of recording material and processing technique.

6

H . M . Smith

The equations describing the diffraction efficiency of the various hologram types are divided into two groups, those for plane holograms and those for volume holograms. This is because the description o f the diffraction process for the two cases is fundamentally different, even though it has been shown that in the common case of amplitude holograms, for most practical recording situations the resulting diffraction efficiences are equivalent [1.15]. This is definitely not the case for phase holograms, however. The distinction between thick and thin' holograms is made with the aid of the Q-parameter defined earlier [(1.3)]. The hologram is considered to be thick when Q > 10 and thin otherwise.

1.4.1 Plane Holograms Amplitude Holograms We begin by assuming an irradiance distribution at the hologram (for a diffuse object) given by H(x) = ]Oo(X)e i~°(x) + Roei"x[ 2 = O~(x) + R02+ 2Oo(x) R 0 cos(cox- ¢P0),

(1.11)

where Oo(x ) and R o are the (real) amplitudes and q~o(X)and cox are the phase of the object and reference waves, respectively. The object is assumed to be diffuse so that both the phase and amplitude of the object wave are functions of the space coordinate x. The average spatial frequency of this distribution is given by

~= ~

~ [co~-~Oo(~)] ,

(1.~2)

where the angle brackets indicate a spatial average. If we take into account the M T F of the recording material, the effective exposure is E = tH = t[(O2(x)) + R z] [1 + mM(g) cos(cox - q~o)],

(1.13)

where t is the exposure time and m is the exposure modulation given by m=

2[(O~(x))R~] 1/2 (Og(x)) + R~ '

(1.14)

and M(~) is the MTF. In (l.14) we have used ( 0 2 ( x ) ) rather than the more rigorous O2(x), and so we are neglecting the self-interference or speckle caused by the diffuse object. However, the effects of the sp,-ckle are not excessive as long as the modulation m is not too large. The modulation of the fringes represented by the cosine term of (1.13) is reduced by the factor M(F), the M T F of the recording material at the average frequency F. This is a good approximation as

Basic Holographic Principles

7

long as the object size is such that it subtends a very small angle at the hologram. If this is the case, q~o(X) is nearly a constant, or a constant plus a term proportional to x, and the bandwidth of the recorded signal is small and centered around 7. If we assume the amplitude transmittance-log exposure curve ( T , - l o g E ) to be essentially linear with slope e in the vicinity of the average exposure E 0 = t[(O2(x))+R2], we can write for the amplitude transmittance

T,(E) = T,(Eo) + c~log(E/Eo),

(1.15)

so that T (x) = T.(Eo) + c~log [1 + mM(v-') cos (cox- (Po)] •

(1.16)

Expanding the logarithmic function, we have Ta(x) = T,(Eo) + 0.43ct [mM(v--)cos(cox- q~o) m2M2(v-) s2, ~co ~cox- ~Oo) + maM3(v) cos 3 (cox - ~Oo)-- ... 7. 3

(1.17)

The T , - l o g E curve is linear only in the vicinity of E o, which implies a moderately small exposure modulation m. Therefore, we must assume the m is small enough that we can neglect all except the first-order term in (1.17) and arrive at

T.(x) = T.(Eo) + 0.43c~mM(7) cos (cox - q~o).

(1.18)

The object wave is reconstructed by illuminating the hologram with the reference wave Roexp(icox), yielding a conjugate image term 0.434 i ~p¢(x)= - ~ - Roamm(F)e ~'~.

(1.19)

The irradiance in the reconstructed field is Hc--R2o[[0"4342~tmM(7)]

(1.20)

and the diffraction efficiency is [0.434 ]2 q = HJR~ = [ - ~ o~mM(~)] .

(1.21)

8

H . M . Smith

Now

m = 2[(02o(x))R2o] 1/2/[(02(x)) + RZo] = 2 ~ / K I+K '

(1.22)

where K is the beam ratio R2/(O2o(X)>. Since we are already restricted to moderately small values of m, K is somewhat greater than unity, and so m ~ 2 / ] / K giving for the diffraction efficiency ~2

r/=0.188 ~ - M2(g).

(1.23)

This equation shows that the diffraction efficiency will be a maximum at an average exposure for which the T , - log E curve of the recording material has maximum slope. Because we have assumed that the exposure modulation m is not too large, (1.23) does not indicate the maximum diffraction efficiency obtainable with thin amplitude holograms. To get an idea of this upper limit, we write for the amplitude transmittance of the exposed and processed hologram

T,(x) = T,(Eo) + T 1 cos (o2x - ¢po),

(1.24)

where T,(Eo) is the average transmittance due to the average exposure E o = t[(O~(x)) + R 2] and T~ is the amplitude of the spatially varying portion of the exposure,

t[ ( O2o(X)) + R Zo]mM(~) c o s ( ( o x - ~Po). To achieve the maximum possible diffraction efficiency, Ta(x) should vary between 0 and 1. Thus

T~(x) = ½ + ½ cos(o)x- q'o) = ~ + ~ 11 ei(,ox- ~oo)+ ¼ e - i(,~x-~oo) .

(1.25)

From this equation it is evident that the maximum diffracted amplitude in either the primary or conjugate image is only one-fourth the amplitude of the illuminating wave. The useful light flux in either image is therefore only onesixteenth of the illuminating flux, yielding a maximum diffraction efficiency of 0.0625. This is somewhat artificial, however, since there are really no practical materials that are linear over an exposure range so large that Ta(x ) will vary from 0 to 1. Some nonlinearity or clipping will alwa~s occur when the exposure modulation gets large. Therefore, the maximum efficiency of 0.0625 cannot be achieved when it is necessary that the reconstructed wave amplitude be proportional to the object wave amplitude.

Basic Holographic Principles

9

Phase Holograms

If the phase of the transmitted wave is p r o p o r t i o n a l to the exposure q~t(x) = yE(x)

(1.26)

then a phase h o l o g r a m results. If E(x) oc [O + RI 2

(1.27)

and O(x) = 0 o ei~'°~x~ R(x) = R o e lax

(1.28)

then Ta(x)= bte i'm(x)

= b, exp(iyO g) exp (iTR~) • exp {2i?OoR o [cos (~oo - fix)] }.

(1.29)

Simplifying the notation we set K = b, exp [i?(O02 + Ro2)] a = 27OoR o

(1.30)

O -~ ~Oo - flx

so that Ta(x ) = K e i.... o.

(1.31)

N o w by using the Bessel function expansions cos (a cos O) = Jo(a) + 2 ~,~= 1 ( - 1)"dz,(a) cos 2n69 sin(acos 0 ) = 2 ~ = o ( - 1)"+ z J2. + l(a) cos [ ( 2 n + 1 ) 0 ]

(1.32)

and the relation e ix = cos x + i sin x

(1.33)

we can write T~(x) = K {Jo(a) + 2 ~ = 1

( - 1)"J2.(a) cos 2nO

+ 2i ~,,,% o ( - 1)" + 2J2. + 1(a) cos [(2n + 1) 6)] }.

(1.34)

10

H. M. Smith

The J,(a) are Bessel functions of the first kind• Each is the amplitude of the n-th diffracted order. The term leading to the images of interest is K[2iJl(a ) cos 6)] which can be written as • /elO+ -io~ 21KJx(a) I 2e -) =iKJ,(a)[ei'~°°-'X) +e-i'~°°-IJx)]. (1.35) These two terms represent the primary and conjugate image waves. The transmission term leading to the primary image is T~(x) = b, exp [i(702o + 7R 2 + n/2)] •J l(2yOoRo) exp [i(tp o - fix)].

(1.36)

When the hologram is illuminated with a wave of unit amplitude, the firstorder diffracted wave has an amplitude T, given by (1.36)• Since we are assuming for simplicity that we have a pure phase hologram, that is, no absorption, b, = 1.0 and the diffracted wave amplitude is simply (Jl(2yOoRo). The diffraction efficiency is equal to the square of this quantity• The maximum value is 0.339, which is considerably higher than the maximum efficiency for amplitude holograms• It will be seen from the following sections that the efficiency of thick phase grating is even higher yet, which explains the very great interest in producing low noise phase holograms• 1.4.2 Volume Holograms Coupled Wave Theory

The preceding theories for thin holograms cannot apply when the diffraction efficiency becomes high, because for high diffraction efficiencies the illuminating wave will be strongly depleted as it passes through the grating• In some way one must take into account the fact that at some point within the grating there will be two mutually coherent waves o f comparable magnitude traveling together. Such an account is the basis of the coupled wave theory, so aptly applied to the problem of diffraction from thick holograms by Kogelnik [1.16]. This elegant analysis gives closed form results for the angular and wavelength sensitivities for all of the possible hologram types--transmission and reflection, amplitude or phase, with and without loss, and with slanted or unslanted fringe planes• The equations also give, of course, the maximum diffraction efficiency achievable when the grating is illuminated at the Bragg angle and the fringe planes are unslanted. The equations are the result of a theory that assumes that the gratings are relatively thick so that there are only two waves in the medium to be considered, that is, that the Bragg effects are rather strong• Nevertheless, the equations are surprisingly accurate over a very large range of Q-values, including values considerably less than 10. For a complete treatment of the theory one should refer to [1.16]. Here we will only outline briefly the underlying ideas of the theory and give the principal results.

Basic H o l o g r a p h i c P r i n c i p l e s

~""

"--

d ~

11

Z

Fig. 1.1. N o t a t i o n u s e d t o d e f i n e a t h i c k g r a t i n g

The coupled wave theory assumes that there are only two waves present in the grating: the illuminating wave C and the diffracted signal wave S. It is assumed that the Bragg condition is approximately satisfied by these two waves and that all other oders strongly violate the Bragg condition and hence are not present. The equations that are derived express the coherent interaction between the waves C and S. Figure 1.i defines the grating assumed by K o g e l n i k for his analysis. The zaxis is perpendicular to the surfaces of the medium, the x-axis is in the plane of incidence and parallel to the medium boundaries, and the y-axis is perpendicular to the page. The fringe planes are oriented perpendicularly to the plane of incidence and slanted respect to the medium boundaries at an angle q). The grating vector K is oriented perpendicularly to the fringe planes and is of length ll~l ~ 2re~A, where A is the period of the grating. The angle of incidence for the illuminating wave C in the medium is O. The Bragg angle is O o. It is assumed that the fringes are sinusoidal variations of the index of refraction or of the absorption constant, or both for the case of mixed gratings. The assumed equations are therefore n o = n -t- n I c o s ( K - X )

(1.37)

a 0 = a + a I cos(K-X),

(1.38)

and

where K. X = cox and co is 2n divided by the fringe spacing in the x-direction. The quantities n and a are the average values of the index and absorption constant, respectively. The slant of the fringe planes is described by the constants c R and c s, which are given by cR = cos O ,

(1.39) K

c s = cos O -- ~- cos O ,

where 13= 2rcn/2, and 2 is the free space wavelength.

(1.40)

12

H. M. Smith

When the Bragg condition is satisfied we have cos (cp - Oo) = K / 2 ~

(1.41)

c R = cos O o

(1.42)

c s = - cos (2cp - Oo).

(1.43)

and

In the case where the Bragg condition is not satisfied, either by a deviation A O from the Bragg angle O 0 or by a deviation A2 from the correct wavelength 20, where both A O and A2 are assumed to be small, K o g e l n i k introduces a dephasing measure (_9. This parameter is a measure of the rate at which the illuminating wave and the diffracted wave get out of phase, resulting in a destructive interaction between them. The dephasing measure is given by (9 = A O. K-sin (q~ - 0 o) - A 2 K 2 / 4 n n ,

(1.44)

where o

(1.45)

A2 = 2 - 20 .

(1.46)

A6)=O-O

and

The coupled wave equations that result from this theory are cgR' +aR = - ikS

(1.47)

csS' + (a + i (9)S = - ikR,

(1.48)

where k is the constant defined by k = r~nl 2

ial 2 '

(1.49)

and the primes denote differentiation with respect to z, and i = ]/S1-. The physical interpretation of these equations as described by K o g e l n i k is as follows : As the illuminating and diffracted waves travel through the grating in the zdirection their amplitudes are changing. These changes are caused by the absorption of the medium as described by the terms a R and as, or by the coupling of the waves through the terms k R and kS. When the Bragg condition is not satisfied, the dephasing measure (9 is nonzero and the two waves become out of phase and interact destructively. The solutions to these equations take on various forms depending on the type of hologram (grating) considered. When transmission holograms are considered, we say the fringe planes are unslanted when they are perpendicular

Basic H o l o g r a p h i c Principles I,OF

"9

I

I

I

I

I

13

I

O.5

O

oX

o,2x

o.4X

o.6x

o,8x

i.ox

i,2x

1.4X

Fig. 1.2. Diffraction efficiency as a function of the optical path variation nld/cosO o in units of the wavelength for a thick phase hologram viewed in transmission

n I d / c o s Oo

to the surface. This condition is described by c R = c s = cos O since q~= rt/2 in this case. I f the Bragg condition is also satisfied, then o f course 19 = 19o. F o r reflection holograms, on the other hand, no slant means that the fringe planes are parallel to the surface, so ~o= 0. I fthe Bragg condition also holds, then c a = - c s = cos O 0.

Transmission Holograms Pure P h a s e H o l o g r a m s . F o r a pure phase, transmission h o l o g r a m the absorption constant a o = 0 and the solution of the coupled wave equations leads to a diffraction efficiency, for the general case o f slanted fringes and Bragg condition not satisfied, given by q = sin2(v z + ~2)1/2/(1 + ~2/v2) V = nnld/A.(cllCs)

U2

(1.50)

= (9d/2c s = A O K d sin (qo - 0 o ) / 2 c s = - A2K2d/87zncs.

In the case for which there is no slant and the Bragg condition is satisfied, the formula reduces to the well-known equation = sin 2 (r~n i d/2 cos (90).

(1.51)

A graph o f this equation as a function o f the optical path in units o f the free space wavelength 2 is shown in Fig 1.2. It is seen that diffraction efficiencies o f 1.0 are possible with this type o f hologram. P u r e P h a s e H o l o g r a m s with Loss. F o r this case we consider the effect o f some loss on a phase hologram. The loss takes the form o f some residual absorption, such as might be caused by a chemical stain that has not been washed out or perhaps

14

H. M. Smith

1,0

I

]

I

I

I

I

0,5

--

~ 1

0

~v~'"lOX 0,2X

t O,4X

I O,6X

q'",--"~- I O, Sh I,Oh

1,2X

Fig. 1.3. Diffraction ficiency

ef-

as a functionof the opticalpathvariation n,d/cosO o in units of the

1,4X

wavelength for a thick phase hologram with loss, for several values of optical density DO

n,d/cos 0o some intrinsic absorption at the readout wavelength. For this sort of grating, a 1 is zero but a is not. The equation for the diffraction efficiency takes the form rl --_e -2atilt°sO

sinZ(v2 + ~2)1/2/(i +~Z/vZ)l/2 (1.52)

v = r~nl d/2 cos O = (_9d/2 cos O = A Ofld sin Oo,

where we assume that the grating is unslanted and that the Bragg condition is not satisfied. The absorption evidenced by the exponential term in front and leading to an overall decrease in the efficiency to Bragg mismatch is not much different from that of the lossless hologram. In the case where the Bragg condition is satisfied, the equation simplifies to q = e - 2,a/cosOo sin 2 (~tnld/2 cos Oo).

(1.53)

The effect of the absorption is simply to decrease the overall efficiency by the exponential factor in front. A curve of this function is shown in Fig. 1.3 for several values of the residual density D o = O . 8 6 8 a d / c o s O o, which is just the optical density measured in the direction of the illuminating wave. A m p l i t u d e H o l o o r a m s . For a pure amplitude hologram there is no modulation of

the refractive index, so n~ = 0. The solution to the coupled wave equations in this case is CR exp. -- ad ?~ ~

+

sinh2(v 2 + ~2)1/2/( 1 + ~2/~,2)

Cs

1)

v = aid/2(CRCs) 1/z

~= ~ad

-

(1.54)

Basic Holographic Principles ,04

I

I

I

15

I =

.o2,

o

I

o.2

0.4

o.6 a , d / 2 cos Oo

o.a

r.o

Fig. 1.4. Diffraction efficiency as a function of the parameter ald/2cosOo for thick amplitude holograms viewed in transmission. The curves are plotted for several values of the reference-toobject beam ratio K, which is related to the absorption constants a and a~ through a/al 2 ~/K/(1 +K). The average specular transmittance of the hologram is exp(-2ad/cosOo) for the case where the Bragg condition is fulfilled but the fringe planes are slanted. F o r the case where the fringes are unslanted but the Bragg condition is not satisfied, the equation for the diffraction efficiency becomes t / = e - Zad/cR sinh2(v / _ ~2)/(1 _ (2/v2)

v=atd/2cosO

(1.55)

~ = (9d/2 cos O - d Ofld sin O o -

I A2 2 2 KdtanO o

and in case the Bragg condition is satisfied this simplifies to r/=e - 2,d!co~e,, sinh2(al d/2 cos Oo)

(1.56)

which is plotted in Fig. 1.4. The m a x i m u m diffraction efficiency is achieved when a l = a and ad/cos 0 o = In 3 = 1.1, and is 0.037. This is considerably lower than the theoretical m a x i m u m for a thin amplitude h o l o g r a m (0.0652). The m a x i m u m is reached when ad/cos 0 0 = 1.1, which corresponds to an average density o f 0.955 (measured in the direction 0 o ) or an amplitude transmittance o f 0.34.

Mixed Holoorams. A mixed h o l o g r a m is one for which there is a phase m o d u l a t i o n in addition to the amplitude modulation. In this case b o t h a~ and n~ are nonzero. This situation is o f some practical importance because any real h o l o g r a m will be, more or less, a mixed hologram. F o r example, for a grating produced on a p h o t o g r a p h i c emulsion there is quite likely to be an exposuredependent variation in the refractive index or a surface relief image in addition to the transmittance variation. This then would result in a mixed hologram. The

16

H. M. Smith

relative contribution o f the phase a n d amplitude portions can be predicted from coupled wave theory. Interestingly enough, it turns out that the contributions o f the phase and amplitude parts are simply additive, at least for the case of an unslanted grating and Bragg incidence. T h e equation for the diffraction efficiency is q = [sin2(z~nld/2cos 0 o ) + s i n h Z ( a l / 2 c O S O o ) ] e -

2 ad/eosOo

(1.57)

where all o f the symbols have been previously defined.

Reflection Holograms Pure Phase Holograms. The general equation for the diffraction efficiency o f a

pure phase reflection h o l o g r a m with slanted fringe planes and n o n - B r a g g illumination is q = 1-1 + (1 - (2/vZff sinh2(v 2 - (2)1/2]- a v = irtnld/2(CRCs) 1/z

(1.58)

( = -- (9d/2c s = A O K d sin(O o -- q))/2c s = ARK2d/87tnCs .

Note that v is real since c s is negative. F o r an unslanted grating and Bragg incidence (1.57) becomes (1.59)

17= tanh 2 (r~nxd/2 cos Oo).

Figure 1.5 shows a plot of this equation. It is seen that it is possible to have a diffraction efficiency o f 1.0. A m p l i t u d e Holoorams. F o r a reflection h o l o g r a m of the amplitude type, where n 1 = 0 and a I is nonzero, the diffraction efficiency for u nslanted fringes (q0 = 0) and Bragg incidence is given by

t l = cs tv +

~- - 1

c o t h ( ~ 2 - v 2 ) 112

v = iald/2(CaCs) 1/2

= D o - i(o

(1.60)

D o = ad/cos 0 o (o = A O f l d s i n O o =

1 A~

~ T

Kd'

Basic Holographic Principles I,O

I

i

17

f

0.5

o o

1,0

3,0

2..0

Fig. 1.5. Diffraction efficiency as a function of the parameter nnld/2cosO o for a pure phase reflection hologram

Trn d / X c o s 8 o I

I

,07 .06 ,05

7] .04

Fig. 1.6. Diffraction efficiency as a function of DI =ald/cosOo (the specular density) for several values of the beam ratio K, which is related to the densities DO and Dj through

,03 I0 .02 .01 0

I 0

1,0

I 2,0

DI

I 3,0

O,/Oo = 2

VKI(i + K)

I f the Bragg condition is satisfied, then this equation simplifies to r/= 012 (2[O 2o + (D 2o - D2~/4)1/z coth(D2o- 02/,)1/1]}- z,

(1.61)

where D 1 = aad/cos 19 o. This equation is plotted in Fig. 1.6. The largest allowable m o d u l a t i o n is for D 1 = D O or equivalently, a 1 = a . In this case the m a x i m u m diffraction efficiency is 0.072, which is achieved in the limiting case D 1 = D O= oo.

Summary Figure 1.7 summarizes the principal results. The n u m b e r s shown are the m a x i m u m theoretical diffraction efficiency obtainable for each type o f hologram. With the exception o f the thick, phase, reflection hologram, each o f the theoretical m a x i m a has been very nearly achieved experimentally. F o r a reason that is a yet unexplained, no holographic material and process have yet come close to the theoretical 1.0 diffraction efficiency for this type o f hologram.

18

H. M. Smith

THEORETICAL MAXIMUM DIFFRACTION EFFICIENCY Hologram Type:

Thin Transmission

Modulation

:

Amplitude / Phase__ Amplitude I Phase__ Amplitude] Phase

Efficiency

:

0. 0625

0. 339

Thick Transmission 0. 037

1. 000

Thick Reflection 0. 072

1. 000

Fig. [.7. Table of maximum diffraction efficiency for various hologram types

Clearly the highest efficiencies are achieved for phase-type holograms, and these can be formed quite readily on many types of holographic recording materials. Also, for each of thehologram types considered, it was assumed that some sort of linear relationship existed between input and output. For the case of the thick holograms it was between the amplitude transmittance and the exposure. Unfortunately, it is impossible in any real system to maintain this linearity over the exposure range required to produce maximum efficiency. Thus in most real situations one has to balance an increase in nonlinearity noise against an increase in diffraction efficiency. According to Kogelnik El. 16], the efficiencies that are possible while maintaining the assumed linear response are smaller by about 50% than the corresponding maximum efficiencies, depending on how strictly linearity is defined.

1.5 Noise The noise associated with a holographic image is any unwanted light that is scattered or diffracted into the direction of the desired image during the reconstruction process. This noise light can take the form of a veiling glare that reduces the contrast of the image, or it can be in the form of an unwanted, spurious image. All of the forms of noise present in holography are signal dependent in that they depend either on the amount or form of the object light ; because of the coherent nature of the reconstruction process, the noise light adds coherently to the signal or image light. The principal sources of noise light are as follows: I) Granularity. When a photographic emulsion is used as the recording material, the information recorded on the hologram is built up from millions of tiny clumps o f silver called grains. These photographic grains appear microscopically as fine black specks on a clear background. When light is transmitted through this pattern it is scattered over a wide range of directions, and this is the light that forms a veiling glare around the desired holographic image. There are some recording materials that are either grainless or essentially grainless, and hence do not scatter light. A thermoplastic material, for example, utilizes the surface relief to diffract the light and the material itself is grainless, anti so one would expect no noise of this type. The photochromic materials have grains that are molecular in size. These are so small that the material is essentially grainless and scatters no light.

Basic Holographic Principles

19

2) Scatterin 9 from the Support and/or Binder Material. Scattering can arise even in the grainless materials because of the optical imperfections of the host material. The photochromics are crystalline materials that are subject to imperfections that scatter light, in the case of the thermoplastics it would be the plastic itself plus the photoconductor layer plus the support material that would scatter the light. In the case of the photographic types of materials one often has.to consider the scattering from the support material and from the gelatin binder itself. 3) Phase Noise. Phase noise is intrinsic to phase holograms, but occurs only in the case o fdiffuse objects. The self-interference of the object light is recorded as a low frequency pattern on the hologram. This low-frequency phase pattern diffracts unwanted light into and around the holographic image.

4) Nonlinearity Noise. Nonlinearity noise arises in cases where the final amplitude transmittance of the hologram is not strictly proportional to the recording exposure. The presence of recorded information on the hologram that is proportional to the second and higher orders of the exposure gives rise to unwanted light diffracted in the image direction. This type of noise occurs mainly when the exposure modulation is high so that the range of exposures exceeds the dynamic range of the recording material.

5) Speckle Noise. This is a type of noise associated with holographic images, but it does not strictly fit the definition given in the first paragraph above. In a strict sense speckle noise is not really noise because it arises precisely because of an accurate reconstruction of the object wave. However, it is noise in the sense that the image is definitely degraded by its presence. It arises whenever a diffuse wavefront of coherent light is limited in extent by the apertures of the system. When this happens the phase undulations of the diffuse wavefront become amplitude variations, which have a granular or salt-and-pepper appearance. However, since this noise is not a function of the recording material, it will be ignored in this volume. A more detailed discussion of the various types of noise is presented with the discussions of the different recording materials in the following chapters and so we will not elaborate more here.

References 1.1 1.2 1.3 1.4 1.5 1.6

D. Gabor: Nature 161, 777 (1948) E.N. Leith, J. Upatnieks: J. Opt. Soc. Am. 52, 1123 (1962) E.N. Leith, J. Upatnieks: J. Opt. Soc. Am. 54, 1295 (1964) M.J. Beurger: J. Appl. Plays. 21, 909 (1950) W.L. Bragg, G. L. Rogers: Nature 167, 190 (1951) H.M.A. El Sum: Reconstructed Wavefront Microscopy,Ph.D. Thesis (Stanford Univ. 1952)

20 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14 1.15 1.16

H. M, Smith

M.E. Haine, J. Dyson: Nature 166, 315 (1950) M.E. Haine, T. Mulvey: J. Opt. Soc. Am. 42, 763 (1952) A.V. Baez: J. Opt. Soc. Am. 42, 756 (1952) G.L. Rogers:Nature 166, 237 (1950) P. Kirkpatrick, H.M.A. El Sum: J. Opt. Soc. Am. 46, 825 (1956) Y.N. Denisyuk: Soviet Phys.-Doklady 7, 543 (1963) P.J. Van Heerden: Appl. Opt. 7, 393 (1963) F.G. Kaspar: J. Opt. Soc. Am. 63, 37 (1973) H.M. Smith: J. Opt. Soc. Am. 62, 802 (1973) H. Kogelnik: Bell Syst. Tech. J. 48, 2909 (1969)

2. Silver Halide Photographic Materials K. Biedermann With 25 Figures

For one hundred years, silver halide gelatin emulsion have been used for recording visible and invisible radiation in general photography and cinemato-graphy, astronomy and spectroscopy, x-ray photography and electron micro-scopy, and in many other fields where information is to be stored and retrieved in pictorial, graphical or digitally encoded form. This chapter deals with the r61e of photographic silver halide emulsions in holographic wavefront recording and reconstruction, a new technique that poses quite different requirements on the material and a challenge to meet them. When the coherent light of the He-Ne laser became accessible for holography about fifteen years ago, the photographic emulsion was the only material readily available that provided the necessary high resolution and sufficient sensitivity to the red light of this laser. Since then, lasers generating radiation of shorter wavelengths have been developed, making other lightsensitive processes useful for hologram recording. A great number of nonsilver photographic materials have been improved or adapted for holography, as to be reported on in the following chapters of this book. Silver halide materials have a long tradition, they are versatile, commercially available with a choice of data and sizes, can be handled and processed with a minimum of equipment, and are suitable for making amplitude and phase, color and Lippmann holograms. Hence, there exists more practical experience with their use and more investigations of their properties have been reported than for other materials. Their sensitivity is unequalled by other materials, achieved, however, by means of the time-consuming wet developing process, which makes it also unlikely that silver halide emulsions ever might provide the possibility of local erasure and rewriting, as desired for optical memories. This chapter is intended to give a state-of-the-art review of silver halide photographic materials in holography with preference to facts and problems of interest to the user. The presentation includes assessment of materials and methods for evaluating their characteristic parameters, and discussion of effects that might lead to properties of the holograms or spatial filters not intended by their designer. Research into basic questions with remote connection to practical applications is given shorter treatment with commented references to the literature.

22

K. Biedermann

2.1 T h e H o l o g r a p h i c P r o c e s s Both amplitude and phase of a wavefield can be stored in coded form only according to Gabor's interferometric two-step process. The requirements on the photographic layer in holography, hence, are as follows. In the first step, the layer has to be sensitive to the wavelength from the laser used and has to be capable of recording the microscopic interference structures without appreciable deterioration. The carrier frequency v around which the image information is encoded is given by v=

sin 0o - sin 0 r [c/mm], 2

(2.1)

where 2 is the wavelength in air and 0o and 0r are the angles between the propagation directions of the object and the reference field and the recording plane normal. For a very simple and usual hologram setup with a He-Ne laser (2 = 633 nm), like for nondestructive testing, the angles may be 0o =0 °, 0r =45 °, which gives v~ 1120 [(cyc./mm)]. For Lippmann holograms, the interference fringes are oriented in the depth of the emulsion, where the wavelength is shorter by the index of refraction, n = 1.64, and 0o~90 °, 0r~ - 9 0 ° ; for a blue Ar-laser wavelength of 2=457.6nm, the recording of v~7170 [cyc./mm] may be required. These two figures give a rough first idea of the resolution requirements. They may be compared with conventional photography or microfilm, which put similar demands on detail rendition at about 40 and 200 [(cyc./mm)], respectively. By this exposure and subsequent processing, changes of the optical properties of the layer have to be introduced, which make the result, a hologram, capable of executing the second step: to spatially modulate an incident wavefront so as to reconstruct or generate another wavefront of certain amplitude and phase distribution. For this process, Gabor [2.1] derived a demand for linear relation between exposure and amplitude transmittance of the developed plate. Fortunately, practice should prove that fulfillment of the rigorous Gabor condition, 7 = - 2, can be replaced by approximately linear transfer even with usual negative reproduction. It is seen that these requirements are quite different from those prevailing in ordinary photography. A large part of this chapter will deal with the behavior of the silver halide emulsion in, and its adaptation to, holography. 2.2 The Silver H a l i d e Emulsion A photographic emulsion [2.2~4] consists of gelatin as a protective colloid in which microscopic or submicroscopic crystals of silver halide, predominantly silver bromide, are precipitated.

Silver Halide Photographic Materials

23

High resolution or high values of the modulation transfer function (MTF) at high spatial frequencies, as required in holography, is a question not only of grain size but still more of light scattering in the emulsion. The index of refraction of gelatin is about 1.5, that of AgBr is 2.25. In conventional emulsions, the size of the embedded crystals is of the order of 1 lam, somewhat larger than the wavelength in the medium, hence Mie theory applies and scattering and light diffusion are strong. In order to decrease scattering, the particles must be made much smaller than the wavelength and Rayleigh theory starts to become applicable. Typical values of the grain size of emulsion for holography are 0.080.03 lam [2.5]. However, the sensitivity of fine grain emulsions is inherently very low. The probability o fabsorbing a certain number of photons is proportional to the projected area of a crystal and its depth, hence to the volume or the third power of its "mean diameter". Some margin is in the intrinsic sensitivity of the single grains. The theories of latent image formation [2.2-4] may be summarized to a very coarse explanation: Absorption of a photon supplies energy to free an electron Br- +hv-*Br + e which can move through the crystal lattice. At one of the crystal imperfections (which have to be suitably distributed through the crystal) it is trapped and attracts an interstitial silver ion e- + Ag+ ~ A g . This single silver atom will trap another liberated electron and the cycle repeats itself several times during the exposure. One single silver atom has a lifetime of about one second, a subspeck of two atoms is stable, a latent image speck of at least three or four silver atoms is necessary for catalyzing development [2.6]. This mechanism of latent image formation explains also that there must be an optimum rate of photon absorption per time interval. In holography with Qswitched pulse lasers, the exposure may last for a few nanoseconds only, and attention has to be paid to possible reciprocity failure [2.7]. The intrinsic sensitivity of silver halides is restricted to the blue and ultraviolet regions of the spectrum. Fortunately, certain dyes absorbing in regions of longer wavelengths, are, when adsorbed to silver halide crystals, capable of transferring the absorbed energy to the crystals for latent image formation. The silver halide emulsion is the only recording material, which, thanks to spectral sensitization, can be used for making holograms with the radiation from the ruby-laser (2 = 694 nm). Figure 2.1 shows examples of spectral sensitivity curves of some emulsions intended for recording holograms at different laser wavelengths.

24

K. Biedermann

'1 ~ 0 300

8E56

400

500

.~

600

[nm]

7oo

ebo

Fig. 2.1. Spectral sensitivity curves of three types of emulsions used in holography: Panchromatic spectroscopic plate Kodak 649-F ; Agfa-Gevaert Scientia ("Holotest") 8E75, sensitized for the wavelengths 694nm o f the ruby laser and 633nm o f the He-Nelaser; Scientia 8E56 sensitized for the wavelengths 454 to 514nm of the Ar laser

The latent image is made visible by development. In the commonly used chemical process, the liquid developer soaks the gelatin and gets the agent in contact with the silver halide crystals. By catalytic action, those crystals containing latent image specks of at least critical size are completely reduced to metallic silver, while the others are not. They are dissolved and removed in the subsequent fixing and rinsing baths. Development of silver halides constitutes an amplification process which is unparalleled by other light-sensitive systems. A silver bromide grain with a volume of 1 p.m3 contains 2.10 l° silver ions which can be reduced after the absorption of a few photons. For this grain, the amplification is about 10 l° ; for holographic emulsions it can hence be estimated to be of the order of 10 6 . This great amplification has to be paid for by the inconvenience and delay of the wet development process and drying. However, there is an important advantage in the latent image, especially in storing many holograms by multiple exposure: The recording medium does not start to modulate incident fields as soon as it is being exposed. Processing can also affect the gelatin which may become tanned. The resulting surface relief modulates the phase of an incident wavefield, an unintended effect which can be disturbing, especially in spatial filters. The result of exposure and development is traditionally presented as the well known D-logE curve, density ( = - l o g transmittance) as a function of the logarithm of exposure. The form and especially the steepness of this function is the result of a number of statistical processes 12.8, 9J--grain size distribution, distribution of number of quanta required for deve~opability, etc. Since, in holography, the D-logE curve should be very steep in the toe (Sect. 2.4.2), emulsions had to be cultivated with as narrow distributions of these parameters as possible.

Silver Halide Photographic Materials

25

2.3 The Practical Procedure of Making Holograms and Spatial Filters In this section, we will deal with some aspects of the practical procedure of making holograms with photographic emulsions. We do not treat general questions of holography, like stability of the setup, coherence requirements, etc.

2.3.1 PhotographicMaterials Available Table 2.1 gives some idea of the choice of photographic silver halide emulsions designed or suitable for hologram recording as compiled at the date of writing. It may be interesting to compare the data for silver halide emulsions with those of the other hologram recording materials as presented in tabular form in I-2.10]. Of the plates and films listed in Table 2.1, certain emulsions and sizes are available on special order only. On the other hand, experimental coatings have been made by both Eastman Kodak and Agfa-Gevaert to customer's request, e.g., with thicknesses exceeding 30 ~tm (see Sect. 2.8). Table 2.1. Commercial silver halide emulsions for holography (sources: manufacturers' brochures, [2.5], and laboratory measurements) Type

Agfa-Gevaert Pan 300 Scientia 8E75 Scientia 8E75B Scientia 8E56 Scientia 10E75 Scientia 10E56 Copex Pan

Emulsion thickness [~tm]

Suitable 2

Exposure

[nm]

[~J/cm 2]

plate plate/film plate plate/film plate/film plate/film film

15 7/ 5 15 7/ 5 7/ 5 7/ 5

panchrom. 633,694

200-400 10

>>2000 > 2000

40(0550 633, 694 400-550 514

30 3 2 0.07

> 2000 < 2000 2000

plate

6

633, 694

20

> 2000

film

9

633

0.4

< 2000

film

5

514

0.05

< 500

Substrate

Suitable for spatial frequencies [cyc./mm]

Eastman Kodak Spectroscopic Plate/Film 649F Holographic Plate 1204)2 High-Speed Holographic Film SO-253 Microfile A H U

Comments: It will be clear from p. 36 that it is the M T F that characterizes the performance of an emulsion at a certain spatial frequency. Hence, here only a very coarse classification is indicated. Agfa-Gevaert materials are now being marketed under the name "Holotest". In this book we continue to use the names under which the materials are identifed in the scientific literature.

26

K. Biedermann

2.3.2 Recording a Hologram Aspects on Material, Size, and Geometry The plate size most commonly in stock is 9 c m × 12cm or 10 crux 12.5 cm (4" × 5"). However, the choice of the material depends very much on the purpose. When, as one example, holograms of three-dimensional scenes are made, viewing becomes a real delight first when the "window" is at least 24 cm × 30 cm wide. For this purpose, plates of the class of least grain size suggest themselves since they show high diffraction efficiency and low scattered flux and ensure brilliant, crisp images. Even some preconditioning (Sect. 2.4.5) may reward the effort with a slight further improvement of image quality. A Deviation on Antirefleetion Treatment For good visual image quality (and also for uniform diffraction efficiency, e.g., when holographic interferograms are to be evaluated by point scanning of the hologram), exposure variations from internal reflection within the emulsion support have to be avoided. The high coherence of the laser light causes light reflected at the rear support-air interface to interfere with the incoming light. The exposure variation may be about + 50 % resulting in a disturbing density variation in the hologram, which then looks like a piece of grainy wood and shows a corresponding variation in diffraction efficiency. Most of the plates can be obtained with and without antihalation backing. However, not all of these antihalation backings appear to be sufficient for coherent systems (as well as the usual antireflection coatings on lenses and beam splitters), where reflections of even as small as 0.25 % still create interference fringes of 10 % modulation. Many suggestions for preventing reflections have been published. A good compromise between expense and efficiency seems to be the application of a black lacquer (even on top of the factory AH-coating), which can be stripped off after processing and rinsing. The graphics industry uses stripping lacquers of this type, but also many other black lacquers can easily be peeled off from glass after having gone through the processing cycle. Good index-matching between glass and backing appears to be achieved by a coating made from 100 g polyvinylalcohol in 11 of water (dissolves slowly, boil for about one hour). The antihalo technique had been developed for making diffraction gratings for spectroscopy in photoresist, where freedom from spurious fields and stray light is crucial. The absorbing dye in the coating must not scatter, hence dyes soluble both in water and polyvinylalcohol have to be added to the liquid, like metanil yellow for Ar-laser wavelengths or methylene blue for He-Ne laser light. The strong film is easily peeled offbefore processing [2.11]. More on Choosing Material, Size, and Geometry As an example of another application of holography, hologram interferometry has quite varying demands. If vibrations of an object under investigation are to

Silver Halide Photographic Materials

27

be mapped with high accuracy, many interferogram fringes must be identified in spite of their irradiance decreasing with the square of a zero-order Bessel function JoZ(g?). In this case, emulsions of very fine grain, like the ones recommended for the display application, are preferable for good signal-tobackground ratio [2.12]. For routine measurements in holographic nondestructive testing (HNDT), on the other hand, where only the presence or basic structure o fan inter ferogram is determined from one fixed observation direction, lower signal-to-background ratio is sufficient. In addition, the hologram area often does not need to be larger than the eye or (TV-) camera lens viewing the interferogram. Medium-speed, perforated, holographic 35-mm film will be an economical choice. A body of a miniature camera 24mm x 36mm or less will serve well for holding and transporting the film. It is appropriate to adjust the camera carefully ill such a manner that the normal to the film plane bisects the angle between object and reference beam. Then, slight motion of the film out of its plane will be essentially along the orientation of the interference fringes in space and will not blur the hologram. (The adjustment is easily done by looking from the reference source via the reflection from a blank film in the camera to the object.) If high dimensional fidelity is needed in the holographic image, distortion from slight changes in film buckling between hologram recording and reconstruction can be minimized by using a good quality camera lens that projects an image o f the object near the hologram plane [2.13]. For reconstruction, a glassless film carrier from an enlarger can be used to hold the film flat. Film can be held more stably and reproducibly for recording and reconstruction, if, instead of using an existing camera body, a holder is made that bends the film around film guide rails that form a vertical cylinder of about 10cm radius [2.13]. While a hologram 24 mm x 36 mm on holographic film is more than a factor often less expensive than a plate 9 cm x 12 cm, for routine recording, e.g., H N D T at a production line, another appreciable factor can be saved by using commercial microfilm. Since the M T F of these films decreases rapidly already at low spatial frequencies (see Fig. 2.10), the angle of view would be too limited. Instead, image plane holograms with minimum bandwidth requirements can be made in an arrangement where the reference source is located in the center of the exit pupil of the imaging system. Overlap of intermodulation and image terms can be prevented by means of a double-slit aperture. Reconstruction and projection of the holographic interferograms is possible with nonlaser light [2.14-].

Intensity Ratio K and Exposure As shown in Chapter 1, exposure of a recording medium to an interference pattern of modulation close to one, especially with an extended object, results in strong stray light from intermodulation and nonlinearity terms. Hence, the ratio K of the intensity in the reference beam to the intensity in the object beam at the

28

K. Biedermann

recording plane, K = l r / I o, can be made greater than one. For values of K up to about 5, the decrease in brightness of the holographic image, viz., diffraction efficiency, is less than reciprocal to K [2.15]. At the same time, much more laser light becomes available in the recording plane and allows one to use shorter exposure times, since losses in the reference beam path are very small compared to those in the path from the beam splitter via the object to the recording material [2.16]. Hence, for recording pictorial holograms, beam intensity ratios of K,,~5 to 15 can be regarded as a good compromise. For holograms to be bleached for phase holograms, K should be chosen larger than 10 [2.17, 18]. It should be borne in mind that only the electric vector component of the object field parallel to that of the reference field contributes to hologram formation (the orthogonal one, however, creates intermodulation and should be eliminated where possible). The exact way is to determine K with a polarizer in front of the detector and with normal incidence for each beam, while for determining exposure, irradiance in the recording plane has to be measured, and that without regard to polarization and origin. The exposure should lead to a mean density of 0.7 0.8 for amplitude holograms, since at that density, diffraction efficiency is maximum [2.19], while for holograms to be bleached the density before bleaching should be greater than 1 or 1.5 [2.16, 19]. For amplitude holograms, exposure time should be adjusted carefully. A deviation from that exposure that leads to maximum diffraction efficiency, by 40 % (photographers would say, half an f-stop), drops diffraction efficiency to less than one-half. It is possible to monitor mean density to its optimum value by adjusting development time. In this way, exposure latitude is increased to about 1:4 (Sect. 2.3.3).

2.3.3 Processing Standard Procedures For normal demands, processing is straightforward and uncritical. However, quite complicated procedures have been published starting with treatments of conditioning and gelatin hardening before exposure and aiming at phase holograms via a multistage conversion process. Ways of making phase holograms in photographic emulsions will be discussed in Section 2.7. It is recommended to develop holograms immediately after exposure, since the extremely fine grain of these emulsions may be subject to latent image fading corresponding to a density difference of up to 0.2 density unit for the first hour of delay [2.20]. It seems that most of the strong metol (elon)-hydroquinone developers used for graphic arts films (and some formulas for paper) yield satisfying results. The important properties for a developer are that it gives very low fog and a steep DlogE-curve which is sharply bent in the toe (cf. p. 35). Eastman Kodak

Silver Halide Photographic Materials

29

Table 2.2. Developerssuitable for processing holograms Agfa 80 Water Metol (Elon, 4-Methylaminophenolsulfate) Sodium sulfite(cryst.) Hydroquinone Potassium carbonate Sodium carbonate Potassium bromide Add water to make

2.5 g

Kodak D-19 750 ml

100 g 10 g 60 g 4g

2g 90 g 8g

1000 ml

50 g 5g

recommends developer D-19, development time 5-8 rain at 20 °C. The author's group prefers the formula Agfa 80, which has a slight advantage over the common other developers with respect to fog and steepness of the D-log E-curve. For convenience, the formulae for the two most recommended developers are reproduced in Table 2.2. In work where high reproducibility of the sensitometric data is required, as for certain spatial filters or for measurement of M T F and other material data, all development parameters should be kept under control. Prepare developer from the formula, not from factory-packed mixed powders, use distilled water and degas it by boiling, avoid bubbles when stirring, agitate during development, and discard developer after use. In Section 2.5.2 we shall report on adjacency effects in hologram development ; we experienced occurrence of appreciable and quite varying amounts of adjacency effects if any one of the recommendations just given was not observed. For general holography, the exact duration of development and the temperature are not critical, but they should be kept within some 10 s and 1/2 °C once optimum exposure has been established. Prolonged development and increased temperature compensate for underexposure (as mentioned in the preceding subsection); they increase diffraction efficiency and granularity and hence scattered flux (see Sect. 2.4). An example for Ta - log E and q-log E curves with development time as a parameter is given in Fig. 2.2. When density is monitored for optimization by adjusting development time, the emulsion has to be transilluminated in some way. The wide choice of emulsions available today, most of them more or less panchromatic, makes the recommendation of a safelight filter for visual inspection impossible. A dark blue-green safelight with maximum emission around 507 ram, the sensitivity peak of the dark-adapted eye, should be acceptable for universal use. A CdS exposure meter, like a Gossen Luna-Pro, is well suited to measure density in safelight illumination, when the distant bulb is imaged onto the photoresistor by means of a condenser lens close to the hologram [2.19]. A special densitometer would use infrared radiation from a photodiode and a phototransistor as a detector.

30

K. Biedermann

tOE 70

f

P.=0,25" w-z,00/cycgr~ •~'.

3' 2

/ o#

q6 0,5 q~

~2 G3p i

I

i

=

&,t._

1o9 E

Fig. 2.2. T~- E and diffraction efficiency curves for Scientia 10E70 plates developed in Agfa-Gevaert G3p for 2, 4, 6, and 12min [2.19]

After development, an acid stop-bath (20 ml acetic acid in 1 1of water) should be applied for about 30 s, followed by a short rinse in water. For fixing, the suppliers recommend Kodak Rapid Fixer for 5 min, or Agfa-Gevaert G 334c for 4 min, respectively. Other film fix formulae can be used as well. The fixing times recommended seem to have quite large safety margin. Fixing for a longer time is useless, but etches the tiny grains of these emulsions and lowers density. The final washing time is 15-25 min; it can be shortened to 5 min after use of an alkaline hypo clearing bath. Residual sensitizing dye in the emulsion can be removed by bathing the plate in alcohol for some minutes. An optimum has been found to be a mixture of 3 parts of ethyl alcohol with 1 part of water I-2.21]. When good visual image quality is desired, care should be spent on drying. Tap water sediments or dust dried into the emulsion scatter light and can hardly be removed by repeated washing. Single drops left on the layer or rolling across it give rise to dark spots looking like miniature footprints of small gnawers. These marks are due to a distortion of the gelatin ; they light up at a different reference beam or observation angle. Inattentiveness can, in this way, spoil a beautiful large display hologram, as there is no way to iron out these marks again. For that reason, it was found worth the effort to give valuable holograms a final bath in distilled water, spray them of f with distilled water from a wash bottle, remove all drops at edges, corners, and clamps, and dry the plates in a cabinet not much above room temperature. If a wetting agent is used with the distilled water, its concentration should be one third of that recommended for film drying (e.g., 1 ml Agfa-Gevaert Agepon/1 1 H 2 0 dest.) in order to avoid scattering from a residual film.

Silver Halide Photographic Materials

31

Special Developers Types of developers other than the rapid developers have not proven useful. For spatial filters and other purposes, extended exposure latitude or dynamic range is desirable. Use of low-~ developers, however, results in loss of sensitivity, extreme decrease of diffraction efficiency, and adjacency effects (see Sect. 2.5.2). Monobath developers, i.e., processing liquids that combine development and fixation [2.22], to our experience, can be formulated for a certain emulsion (or perhaps a batch of that emulsion) and rigorously controlled conditions. The slightest deviation, however, is liable to result in failure due among many other reasons to dichroic fog. The very strong nonlinear behavior of such a monobath developer has been used to increase the dynamic range of a complex spatial filter for image deblurring [-2.23]. Similarly inconsistent results have been allotted to studies for reversal development procedures. Even if a fair macroscopic D-log E curve had been achieved, holograms could fail to show the diffraction efficiency expected from that curve (cf. Sect. 2.4.1). It seems that the very narrow size distribution of the extremely small grains in the hologram emulsions is very responsive to the silver halide solvents present in monobath and reversal developers. Also use of reducer (e.g., Farmers reducer) on overexposed holograms or in attempts to change the D-log E curve did not give improvements in diffraction efficiency. Improvement of diffraction efficiency from addition of silver halide solvents to normal chemical developers has been reported by Smith et al. [2.24].

2.3.4 Reconstruction There are two points deserving a short discussion under this heading : avoiding effects from gelatin surface relief and choosing material for photographing holographic images. Amplitude holograms in photographic emulsions do in reality show a complex transmittance distribution due to a phase modulation at index of refraction variations within the gelatin layer and at a surface relief(cf. Sect. 2.5.3). In certain applications, holograms are designed to generate well-defined wavefronts, e.g., matched spatial filters or computer-generated holograms for spatial filtering or testing aspherical optical elements. Little can be done about the internal phase image, which, fortunately, has much less effect than the gelatin surface relief. The phase changes from the surface relief and also from the thickness variations of the glass plate or film substrate are eliminated by means of a liquid gate. The outer surfaces of the windows are optically flat and parallel to one another, and as immersion liquids matching the index of refraction of the developed layer (n~ 1.52), among others, ethyl benzoil acetate (n = 1.523) [-2.18]

32

K. Biederrnann

has been used. In [2.25] a number of immersion liquids, for both dry and wet film, have been investigated. It has also been recommended that intermodulation noise can be decreased by coating the hologram with a lacquer primarily intended as a UV-absorbing layer for color prints [2.26] (cf. Sect. 2.5.3). Photographing images from wavefront reconstructions differs from ordinary photography in two aspects (aside from the fact that the camera can be used without a lens when a real image is photographed): the monochromatic light and laser speckles have to be taken into account when choosing the film. Film speed indication in ASA or DIN is related to exposure with a standardized continuous spectral distribution ("mean daylight"). Very few conventional panchromatic films show appreciable sensitivity at the krypton line 647 rim. The neon line 633 nm is at about the edge of usual sensitization curves and the speed of films with equal ASA number may come out quite different. It may also happen that the dip between the intrinsic sensitivity of the silver halide and the green sensitizer may fall somewhere close to the 514nm argon line. Exposure meters work well, once they have been calibrated to a certain film at a certain wavelength. In monochromatic light, images of diffusely reflecting objects are inevitably disturbed by speckles [-2.27]. When viewing a hologram, stray light from the plate will be one more source of speckles of high modulation (cf. Sect. 2.4.3). The size of the speckles is of the order of J=stop times wavelength. Hence there is a trade-off: no increase in depth of field without increased "graininess" in the picture. When recording holographic interferograms with a camera 24 x 36 mm 2, f: 5.6 gives just perceptible speckling at eight times enlargement. This means also that there is no point in using slow fine grain film; films of 100 to 400 ASA, like Agfapan 100 and 400 and Kodak Tri-X, proved both adequate and convenient for 2=633 nm. In about the same sensitivity class is Kodak Photomicrography Monochrome Film $O-410, which, due to increased y, is particularly suitable for enhancing fringe contrast when photographing holographic interferograms of objects vibrating at high mechanical amplitudes. Photographing holographic images with color reversal film makes it quite apparent that holography is able to reproduce much higher object luminance ratios than common photography. In order to enhance color saturation, color reversal films have increased ~/-values (up to -1.6). This type of tone reproduction does improve fringe visibility in (correctly exposed) holographic interferograms, but spoils highlights and shadows in the color slides of holographically presented technical subjects.

2.3.5 Real Time Interferometer with in Situ Development Users of hologram interferometry would like to do their experiments "in real time", i.e., to observe the interferograms of an object under deformation or vibration at the same time as these changes are executed. Photographic

Silver Halide Photographic Materials

5•

33

3!

3( o 4 2 ~.

15

Ic ? 4 2

s

Development

,; Rinsing

,'s

Fixation

|1

20 215 t [mini Washing

Fig. 2.3. The thickness Z of a Scientia 8E70 layer during processing as a function of time and solutions. Double vertical lines indicate change of solution. The left ordinate relates actual thickness Z to thickness Z 0 of the dry emulsion layer [-2.28]

emulsions have the disadvantage of a delay of at least 20 min after exposure for processing, drying and relocating the plate in the hologram setup so as to bring the reconstructed and the actual object fields into register. This time gap can be shortened, when the plate is developed in situ, eliminating relocation, and still more when drying is disposed of by having the plate in a swollen condition in a liquid gate during both exposure and reconstruction. Several liquid gate plate holders have appeared on the market. The process, however, is not a trivial one and considerable gain in time and diffraction efficiency can be made by using an optimized procedure [2.28]. The procedure consists of filling the liquid gate with developer, which swells the emulsion to four to seven times its initial thickness, exposure, rinsing, filling the gate with fixer, and reconstruction with the plate in the fixer. For optimum results, developer and fixer have to be matched in two respects. For fulfillment of the Bragg condition, the gelatin layer has to have the same thickness during exposure in the developer and during reconstruction in the fixer. (Figure 2.3 gives an idea of the thickness variations in an ordinary processing cycle.) For equal optical path length through the cell at both occasions, the index of refraction of both solutions should be equal. Reference [-2.28] gives formulae for a rapid developer and a matched fixer, and describes in detail the measures for achieving fulfillment of the Bragg condition with emulsions of different swelling properties. Apart from this inconvenience, these swollen holograms have advantages, e.g., suppression of the intermodulation term. With the formulae elaborated in [2.28-1, a gain in speed by a factor of 2-3 due to hypersensitization and a time interval of 100-180 s between exposure and start of interferometric evaluation have been achieved.

34

K. Biedermann

2.4 Characteristic Parameters of Thin Amplitude Holograms and Their Evaluation The mathematical formulation of the principle of holography (Chap. 1) shows in a clear and convincing way that, upon reconstruction, one of the fields emerging from the (fictitious) hologram is proportional to the original object field. In this section, we shall go just one step from the abstract principle to practical realization and analyze what determines the proportionality factor in the case of a thin, pure amplitude hologram of low modulation in a photographic layer. 2.4.1 The Two-Step Transfer Process

Figure 2.4 shows the transfer of a signal from exposure to density of transmittance for a negative material according to Frieser's two-step model [-2.9]. When the emulsion is exposed to the interference pattern containing the holographically encoded information, light spread within the emulsion lowers the modulation of the signal. As in conventional photography, this change in modulation is suitably described as a function of spatial frequency v [cyc./mm] by means of the modulation transfer function (MTF), M(v). In the case of contact copying holograms with incoherent light or demagnifying computer-generated holograms to final size, the M T F of this process (e.g., also the M T F of the reduction lens) has already affected the incident exposure ; the cascaded MTF's are multiplied. This first step is a purely optical process linear in intensity. In the second step, effective exposure is transferred to density via the D-logE curve (a relation that holds strictly only for large uniformly exposed areas, el. Sect. 2.5.2). Since, in amplitude holograms, the amplitude of the incident reconstructing field is modulated, instead of density D amplitude transmittance T., is appropriate iT.I =

1/~

= lO -~/2 .

The diffraction efficiency of a thin amplitude hologram is given by (1.21) r/= [½-0.434. c~(/~),m(v).M(v)] 2

(2.2)

Diffraction efficiency of thin amplitude holograms is proportional to the squares of the macroscopic characteristic c¢(/~), the input modulation, and the MTF. These functions will be discussed in a little more detail in the following sections. 2.4.2 The Macroscopic Characteristic

In the beginning of holography, the demand for linear transfer from exposure to amplitude transmittance [-2.1] suggested the use of the plot T, vs. E for characterizing the macroscopic transfer by photographic emulsions. However, it

Silver Halide Photographic Materials ~#! i

Io

\

Io4

D"

35

~2'

~

t

Io9 E

p(~')= & (~,).M(,9

.oo(v )

t

A Io9 E

Fig. 2.4. The relation between exposure E and density D or amplitude transmittance T. in the developed hologram according to the twostep model. [c~I is the derivative of the T~-log E function [2.29]

has been shown [2.15, 29] that, in fact, the plot T~vs. logE is more appropriate with respect to diffraction efficiency. This presentation, fortunately, also avoids some problems of the T,-E characteristic. In the T,-logE plot, emulsions of different sensitivity or different developers can easily be compared in the same diagram ; the signal amplitude does not change in proportion to mean exposure, rather modulation or A logE can move along the IogE abscissa to explore diffraction efficiency as a function of mean exposure. The important characteristic for diffraction efficiency is the function c~(E), the derivative of T. with respect to logE [2.15, 29], since ~/~c~2(E) { dT~ / 1,110 ~(E)= \dl~gE]~ = - 2- ' T~(/2)'7(/2)"

(2.3)

The second relation indicates the interpretation that diffracted flux is proportional to the square of the local gradient 7(E) of the D-log E-curve at any working point attenuated by the mean intensity transmittance of the hologram. The dependence on these two variables that move into opposite directions with increasing exposure makes clear that the maximum of diffraction efficiency will be obtained in the toe of the conventional D-log E-curve, that maximum 7 in the straight-line portion of the D-log E-curve is of less interest than a steep bend in the toe, and that fog (base density) should be as low as possible. Figure 2.5 shows especially for this chapter measured T , - l o g E and ~2 _ logE curves for a number of materials available at the time of writing. It can be seen that the maximum of c~2 of the different materials is roughly between 1 and 3 with a corresponding effect on diffraction efficiency. Interestingly, the transmittance value at which the maximum occurs is about 0.4 with very little variation between different emulsions and also development procedures, as

36

K. Biedermann tw2

50-253

/

//,


V,//g Fig. 2.9. Principle of the MSSM for scanning a sample in plane SH 4 with two-beam interference fringes. PH indicates a phase shifting device, IS is a detector with an intergrating sphere in contact with the sample [2.391

In principle, the sample, having been exposed to two-beam interference and developed, is irradiated by a two-beam interference distribution of the same spatial frequency and orientation again [2.41]. All the light transmitted by the sample is collected by an integrating sphere, as outlined in Fig. 2.6c and shown in more detail in Fig. 2.9. When the phase of one of the interferring fields is changed, the interference pattern moves across the sample and the light flux detected in the integrating sphere varies periodically. The working principle of this method can be treated in several ways. Scanning the sample with an sinusoidal irradiance distribution many periods wide can be compared to the common microdensitometer principle. This interpretation gave the name "Multiple-Sine-Slit Microdensitometer (MSSM)" to the instrument [2.35]. We may also note that the transmittance function of the sample is multiplied by the cosine function of the two-beam interference, and then the flux resulting from the product is integrated over the entire sample by the integrating sphere. Hence, the instrument performs a Fourier analysis of the transmittance function of the sample [2.42]. We can regard this operation as a cross-correlation as well, or as scaling down of high spatial frequencies to a moir6 fringe of sufficiently low spatial frequency to be conveniently scanned by the aperture of the integrating sphere. Finally, the principle can also be treated as diffraction of two coherent fields at a complex grating and subsequent addition of the diffracted fields while the relative phase of the incident fields is changing [2.43]. Also, from this model, conditions can be derived for measurements suitable to separate the contributions of the amplitude and the phase structures to the total diffracted flux [2.44] (Sect. 2.5.3). Any of the derivations yields as the final result for the total flux detected qS,ot(v, Aq0)= 2- ~b. {q(0) + [q(v)/2]. cos Aq)},

(2.6)

where 4> is the flux from each one of the irradiating fields measured without sample, AO~ is the momentary phase difference between the interferring fields, q(0) is the Fourier coefficient of frequency zero, i.e., the mean intensity transmittance of the sample, and q(v) is the Fourier coefficient of the intensity transmittance distribution for spatial frequency v of the scanning interference

Silver Halide Photographic Materials

43

M I

8E?O ,,l=633 nm

0.5

0

o ....

1o'oo

doo

Fig. 2.10. Typical MTF's of three different kinds o f emulsions : Gevapan 30, a plate of 23 DIN~_ 160 ASA for pictorial photography ; Agepan FF, a microfilm ; Scientia 8E70, a Lippmann-type plate optimized for hologram recording at 2=633 nm

[2.103

field. We see that only intensity transmittance is represented, not a possible imaginary part of the transmittance fields distribution. In the measurement, only the maxima and minima of q~(v, A~o) have to be recorded and the transmittance modulation m(v) of the frequency v in the sample is simply re(v) = q(v) = 2. 4~.... - q~''~" q(0) 4'm. + 4'.,,. '

(2.7)

It is seen that instrument data do not enter the relation and that the output signal of the MSSM is independent of spatial fl'equency. Since, as indicated in Fig. 2.6, the method has a narrow-band characteristic similar to the diffraction method, granularity noise is suppressed and signals of very low modulation can be measured with good accuracy, such as the higher harmonics generated by nonlinear transfer. Due to nonlinear transfer, only for transmittance modulations re(v). 0 . 2

a

• ~ 21 [ 3.e

""--. "~"

" " "-.. x ' " % , .~ , \~ "~,~,

z

%

x FI~ED

""~."...

u_i_ 0.I

or \xx"~

0

I

I

INTENSITY [ 2150 1 230

~ -"~L."--~.

~-

SENSITIVITY

Lo,No 7 5 0 - 3

CaF2:

I

I I I I I[ I0 2

I0

,roW/era 2 ,,

', "

0.3 " TIME

, s

%

I

I

I

I I I Iil

I

I

1 I 11 I

10 3 EXPOSURE

lO 4

( m J / c m ~-)

Fig. 5.11. Erase-mode sensitometric characteristic of a CaF,:La, Na wafer, showing extensive validity of time-intensity reciprocity

ERASE

MODE

02 z I_)

SENSITIVITY

CoF2:Ce,No 751-2 FIXED INTENSITY f 9'000

t

d ,

~.,

•

•

o %..

,~°"

I

I

I

I

I

I I I

2

E

"

[ME

"

.~....~.~.,~.

o

I

I 3

t

I--

IO

rnW/crn

150

I

I

I

]

I

I I Ir

I0 z

I03 EXPOSURE

I

I

I

I

I

II

IO 4

{ m J / c m 2)

Fig. 5.12. Erase-mode sensitometric characteristic of a CaF,, :Ce, Na wafer, showing extensive validity of time-intensity reciprocity

CaF z : La, Na and CaF 2 : Ce, Na Such sensitometric characteristics for p h o t o c h r o m i c C ~ F : are s h o w n in Figs. 5.11 and 5.12. The solid points indicate the erasures induced in two C a F 2 wafers by exposure for various times to erase beams o f selected Jixed intensities. The abscissae are the corresponding erase exposure energy densities. These points

Inorganic Photochromic Materials

147

,o~

~

-

-

I

ERASE I MODE RECIPROCITY

iO 2

I0 PROCITY

F-

1.0

OI

0,01 0 I

, , ,,,,,d I0

........ ERASE

i I0

....

INTENSITY

,,,H I0 ~'

,

, ,,,,.,i

Fig. 5,13. Erase time T~,.z (to 1/2dDmJ versus erase beam intensity for four wafers of C a F 2 : La, Na

...... I0 :~

104

I m W / c m z)

consitute a straightforward replotting of selected sensitivity curves from Figs. 5.6 and 5.7, respectively, with beam intensities spanning approximately three decades. In each case, the several separate curves are indeed well represented by single sensitometric characteristics. With few exceptions, the plotted points along the central linear regions of these characteristics deviate from the curves drawn by less than ___10 % in exposure or _+5 % in optical density. Thus, in this intensity range, time-intensity reciprocity does hold, and these single characteristic curves provide condensed displays of the sensitivity data contained in the families of curves in Figs. 5.6 and 5.7. The open-circle points in Figs. 5.11 and 5.12 indicate the erasures induced in selected Jlxed times by erase beams of various intensities. These points, also directly transposed from Figs. 5.6 and 5.7, sample ten or more different intensities in each case. Their close agreement with the previously determined sensitometric characteristics is a further demonstration of the validity of timeintensity reciprocity for these wafers in this intensity range. Because of the effects of room temperature thermal erasure, time-intensity reciprocity cannot be expected to hold for arbitrarily low-erase beam intensities. The primary effect is that, as thermal processes begin to contribute, a given integrated erase energy density appears to induce greater erasure. The x-points in Fig. 5.1 l were determined in the same manner as were the solid points, but for an erase intensity smaller by another factor often, 0.3 mW/cm z. It is clear from Fig. 5.6 that the time required for appreciable erasure at this beam intensity is also that required for thermal erasure to become significant. The accompanying reciprocity failure is evident in the x-point curve in Fig. 5.11. The "reciprocity characteristics" of Figs. 5.13 and 5.14 show time-of-erasure as a function of erase beam intensity for each of the CaF 2 sample wafers listed in

148

R. C. Duncan, Jr. and D. L. Staebler IO

I

I

I

10 z

IO

CoF. ~c..,o o.o.s6,.,,~ (ol

%\ \ Nie,,, \

(*)

"~'~,

1.0

lo.3z

"

O,I

0,01

........

0 1

I I

........

0

F

,

, ......

I0 ERASE

INTENSITY

I

........

10 2 (mW/cm

I

I0~

Fig. 5.14. Erase time 7"1/z (to 1/2ADm,x) versus erase beam intensity for three wafers of C a F 2 : Ce, Na

. . . . . .

104

~ )

Table 5.2. The time-of-erasure used is Tl,z, the time required for the readout optical density to be reduced to half its initial (saturated) value. The range of erase intensities spans nearly four decades or more. "True reciprocity" is indicated by straight lines with slopes of - 1 . 0 . For erase beam intensities greater than about 10 m W / c m z, almost the perfect inverse relationship required for true reciprocity is exhibited. Reciprocity begins to fail very gradually for smaller intensities, occurring earlier (i.e., at higher intensities) for C a F 2 : La, Na than for CaF z : Ce, Na, and slightly earlier for the thinner wafers than for thick ones. The values of T~/2 corresponding to the first signs of reciprocity failure are T,/z ~ 10 ( _ x 3) s for CaF 2 : La, N a wafers and T1.¢2~20(+ x 2 ) s for C a F 2 :Ce, Na. In the intensity range between 1 and 10 m W / c m 2, i.e., for approximately the first decade of reciprocity failure, T~/z varies as about the inverse 0.9 power of erase intensity. The values of T~/z,,, . . . . ~corresponding to r o o m temperature thermal decay alone are about 2.6 x 104 s for CaF z : La, Na, about 4 x 104 s for CaF 2 : La, and about 4 x 105 s for CaF 2 : Ce. Thus, gradual reciprocity failure first begins while the ratio T~/z/T~/z,th . . . . ~ is still only about 10 -3 or smaller. S r T i O 3 : Ni, Mo, AI and C a T i O 3 : Ni, M o

Sensitometric characteristics for photochromic titanates are shown in Figs. 5.15 and 5.16. The solid curves indicate the erasures induced in two titanate wafers by exposure for varying times to erasure beams of selected fixed intensities. The abscissae are the corresponding erase exposure energy densities. Thus, selected sensitivity curves of Figs. 5.8 and 5.9 respectively, corresponding to beam intensities spanning more than three decades (more than four in Fig. 5.16), are

Inorganic Photochromic Materials

ERASE 0.5

MODE S E N S I T I V I T Y

Sr Ti 03:Ni,Mo, At S T - 2 - I0 FIXED INTENSITY (SOLID CURVES)

z

=
10, the maximum efficiency approaches 100 % [5.34], the value for a purely phase grating. The problem is that the sensitivity decreases because of the drop in absorption away from the bandpeak. From the data of Tomlinson [5.34], one can show that for ~ -~ 10 (the case where r/...... ~50%), the sensitivity becomes only 0.40 of the value at the bandpeak. The situation becomes worse even further from the peak; at ~o=~37, qm,x ~ 80%, but the sensitivity is down to 0.04 of its value at the peak. Thus, there is a clear tradeoffbetween maximum efficiency and sensitivity. The optimum use of this tradeoff in a given application would require a selectivity in wavelength that is not generally available. The rapidly improving dye laser technology could prove useful here. Scrivener and Tubbs [5.39] used anomolous dispersion to record phase holograms in KCI. They produced diffraction efficiencies of up to 4.2 %, larger than that allowed by purely absorptive gratings. The wavelength for storage (514.5 nm) was close to the half power point of the F-I and, a point where the refractive index variation has a large effect compared to the absorption. Indeed, in previous experiments with KBr [5.40-[ the same authors had found a maximum efficiency of only 2.3 % ; there the storage wavelength (632.8 nm) was close to the peak of the F-band, and the anomalous dispersion had little effect.

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155

5.3.3 Storage Capacity Since the resolution of these materials is not limited by grain size, the storage capacity of a thick crystal is determined primarily by the number of holograms which it can contain. This, in turn, depends on the diffraction efficiency needed for a suitable signal-to-noise ratio in readout ; there is usually a tradeoffbetween the number of holograms stored and their diffraction efficiency. To calculate this tradeoff, we consider a set of N purely absorption holograms, each one with an absorption modulation o f a 1. For this case, the average absorption coefficient is given by a = N a ~ . Placing this in (5.3) and maximizing, we find that the maximum efficiency of each hologram is r/re.x = [(2N + 1)/(2N - 1)] - zU(4N 2 - 1)- t

(5.11)

For N>> 1, (5.11) becomes q ..... = e- 2/4N 2 =(1/N 2) x 3.4%.

(5.12)

Each hologram has an "inherent" diffraction efficiency of I / 4 N 2 that is attenuated by the crystal's transmission of e x p ( - 2 ) . Clearly one pays a large price for increasing the number of holograms. For N = 100, the r/of each is only 3 . 4 x 10-4%.

This can, in principle, be improved by the anomolous dispersion effect discussed by T o m l i n s o n [5.34]. Following his theory and considering only efficiencies much lower than 100%, we find r1 = ( e - Z / 4 N Z )

(1 + 02).

(5.13)

The absorption components maximize as before [e.g., the transmission of the crystal is still e x p ( - 2 ) ] , but the efficiency is enhanced by the factor (1 + ~92). At ~ = 10, r/m,x~ 3.4%(I0/N) 2. The efficiency for a given number of holograms is increased by a factor of 100 over that allowed by absorption effects alone. As discussed in Section 5.3.1, such an improvement is at the expense of sensitivity. In the above discussion, it was assumed that the material had sufficient recording range (maximum absorption change) to store the holograms. The required range can be calculated from the maximum possible absorption introduced by all of the holograms. This occurs where they all add up in phase. This summation added to the average absorption gives Aa o = 2Na I

,

(5.14)

where A a o is the required recorded range. From the value of A a o d required for the maximum efficiency derived above, one can show that Aa o =(2 cOS0o)/d.

(5.15)

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For a 1 cm thick crystal, this becomes Aa o = 2 cm- i, a value that can be easily obtained in most photochromic materials. A larger recording range is required if the efficiency enhancement via anomalous dispersion is to be used. This is because the wavelength required for a large effect is at the side of the absorption band. For ~o~_ 10, the absorption at this wavelength is down to 0.039 of the value at the bandpeak [5.34]. Thus, the maximum recording range (at the peak) must increase by a factor of ~27. These recording range arguments hold true only for uniform gratings. In practice, the gratings are not uniform. The ones recorded first are stronger at the front than at the back of the crystal. This is due simply to the attentuation of the storage beams by the sample's absorption. Thus, successive storage steps in the same crystal will eventually overexpose the front portion of the crystal. This will eventually destroy the holograms stored there, The onset of this loss is a practical limit to the number of holograms that can be superimposed by a sequential storage process. The best reported result is storage of 100 holograms in photochromic glass by Friesem and Walker [5.41]. 5.4 Photodichroics

Photodichroic materials store information through selective alignment of anisotropic absorption centers. This storage process was first proposed by Schneider [5.42]. It was later demonstrated experimentally by Schneider et al. for bit storage [5.43] and by Lanzl et al. for hologram storage [5.44]. The alignment of centers is induced by exposure to linearly polarized light. It is observed as an induced dichroism in the optical absorption of the host crystal, i.e., the exposed crystal selectively absorbs light only of a certain polarization. Since this is a storage process that involves localized color centers, it has many of the features (and disadvantages) of the photochromic process discussed above. There are, however, some important improvements. The main one is that the material is, in effect, bidirectional, i.e., a sample's preferred orientation for absorption can be switched between two orthogonal directions. Thus, a single laser can be used for all steps (storage, readout, and erasure) ; only the direction of linear polarization is changed. In addition, there are new techniques, not available in the photochromic materials, for nondestructive readout. In the following, we present the storage model for these materials and then discuss their application for holographic storage. 5.4.1 Model

A good example of photodichromism is the center com~nonly referred to as the F A center, an alkali halide F center perturbed by a nearest neighbor substitutional cation impurity [-5.45]. As shown in Fig. 5.19, this center is anisotropic, i.e., it has an axis of orientation. The storage process is the realignment of the centers into a new direction.

Inorganic Photochromic Materials

@c,FA

CENTER

®K+

EXCITED

STATES

®No+

~B ~

(z)

BAND

AND 1

2:

GROUND S T A T E '

Fig. 5.19. Schematic diagram of F A centers in Na-doped KC1 crystal, showing two possible orientations of an F^ center. The arrows show the polarization direction of light absorbed by band 1 in Fig. 5.20. The middle configuration shows the midpoint of the reorientation process

R EORIENTATION

(x,y)

157

ABSORPTION SPECTRA

2

Fig. 5.20. Schematic illustration o f the model tbr photodichroic behavior, showing optical transitions and corresponding absorption bands for an F A center. The bands are broadened by thermal vibrations

To understand this process, and how it is read out, one must first consider the optical absorption properties of the F Acenter. Its absorption arises from allowed transitions of the trapped electron from a single I s-like state to three possible 2plike states, each one aligned along one of three mutually orthogonal directions. In the unperturbed center these excited states are degenerate (all have the same energy) because of the symmetry of the center; the nearest neighbor cations are at corners of an octahedron. In the F A center, however, the electron is perturbed by an impurity at one of the corners of the octahedron (e.g., a Na ion replacing a K ion in KC1). Thus, its absorption is anisotropic, i.e., it exhibits linear dichroism. The reason is pictured in Fig. 5.20. The perturbation splits the excited state energies; the z excited state aligned toward the impurity is lowered relative to the other two states, x and y. This splits the F band into two separate highly anisotropic absorption bands (I and 2). Band I absorbs light polarized parallel to the perturbation direction; band 2 absorbs light perpendicular to it. The presence o fanisotropic F a centers in a cubic crystal such as KCI does not necessarily lead to linear dichroism. A given center can be aligned along any one of three equivalent directions. Normally, the directions are equally populated. This averages out the microscopic anisotropy, giving a net absorption that is perfectly isotropic. A crystal exhibits linear dichroism only if the orientation of the centers is changed. In photodichroics, this is done by exposure to linearly polarized light. Only centers aligned in the proper direction absorb the light. Upon absorption,

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their activation energy for reorientation (,-~0.1 eV) becomes much lower than normal ( --~ 1 eV for centers in the ground state). They can thus freely reorient into another direction at temperatures greater than ~ 170 K. Upon relaxation to the ground state, the realigned centers are frozen in. The result is a spot of linear dichroism that can remain for weeks at room temperatures. L i i t y [5.45] has shown that the center reorients by hopping the vacancy around the impurity. This process is pictured in Fig. 5.19. A horizontal center (on the left) is exposed to horizontally polarized light that is absorbed by band 1 (Fig. 5.20). Upon absorption, the center rotates into a vertical orientation in which it no longer absorbs the light. The net result of such an exposure is to place most of the centers in the vertical direction. The crystal then exhibits linear dichroism. In formation stored in this manner is read out as a change in the absorption of light of a given polarization, either directly or via diffraction. Refractive index changes (i.e., birefringence) due to anomalous dispersion can also be used [5.46]. Other anisotropic centers can be used in this manner. They include the M center [5.43] (two adjacent F centers) and the M A center [5.47] (an M center perturbed by an alkali-ion impurity). The photochromic center in rare-earthdoped CaF 2 shows similar reorientation effects [5.20], but it has not been evaluated for photodichroic storage applications.

5.4.2 Hologram Storage The F A center in Na-doped KCI is by far the most popular photodichroic material for holographic storage applications. L a n z l et al. [5.44] found a sensitivity for the photodichroic process three orders of magnitude higher than that for the photochromic process in similar materials. Only 10 mJ/cm 2 of incident light (at 632.8 nm) was needed to produce an optical density change of 0.4. The high sensitivity was ascribed to a near unity quantum efficiency for reorientation (centers rotated per absorbed photon) at room temperature. Holographic images of excellent quality were recorded with 15 mJ/cm 2 (at 632.8 nm) and then read out at the same wavelength. Since readout was done at room temperature, an attenuated beam was needed to prevent hologram degradation. They pointed out, however, that nondestructive readout is possible at temperatures lower than 150 K. R o d e r [5.48] later studied the volume storage capabilities of the same material. He found that the angular sensitivity of a hologram recorded in a 1.6 mm thick sample was ~ 2 5 % smaller than expected. He suggested that this was due to the attenuation of the storage beams as they traverse the crystal. The hologram was stored primarily toward the front part of the crystal, thus reducing its effective thickness. The maximum diffraction efficiency was only 0.15 %, but the sensitivity was high;it required only 5 mJ/cm 2 at 632.8 nm. He also recorded up to eight holograms at different angles in the same crystal and found a severe degradation problem. The first recorded hologram is bleached as the subsequent recordings begin to overexpose the front part of the crystal. Eight such recordings decreased its efficiency by nearly a factor of 20.

Inorganic Photochromic Materials

159

Blume et al. [5.49] described a system for document storage and retrieval using F Acenters in KCI. Holograms were stored at different angles, 14 min apart, with the 514.5 nm line of an argon laser. There was negligible crosstalk between the holograms upon readout with the same wavelength. Readout at 55 K was practically nondestructive. The results demonstrated that superposition of 100 holograms seems to be feasible, each one requiring an average exposure of 1 mJ/cm 2. A unique feature of their system was the use of orthogonally polarized object and reference beams. In this method, the optical interference pattern is composed o f periodic patterns of alternating polarizations. As a result, the storage process does not lead to a bleaching process analogous to that in photochromic materials. Thus, the overall optical density of the crystal does not change during storage. This may be particularly helpful during multiple storage (see Sect. 5.3.3) but cannot eliminate erasure during storage. The beams used to record a new hologram will erase holograms previously recorded at different angles. This method also allows suppression of scattered noise during readout. A linear polarizer is positioned to pass the reconstructed image but block the light scattered from the orthogonally polarized reference beam. Dichroic absorption by M centers and M A centers has also been used for information storage, although most of this work has involved direct storage, i.e., bit storage [5.43, 50-52]. Nevertheless, holographic applications of these have been proposed [5.46, 52] with particular emphasis on the possibility of phase holograms due to anomalous dispersion [5.46]. Indeed, phase holograms have been recorded using the M center in NaF, but with e fficiencies of only up to 0.8 % [5.39]. M-center storage has the disadvantage of a low reorientation efficiency [5.43], and this leads to storage sensitivities lower than that for F Acenters [5.44]. An important advantage of M and M A centers is the possible use of suppressive writing effects [5.47, 52] for nondestructive readout. Here, the reorientation process is suppressed by a long wavelength (e.g., 820 lam) light beam. The beam can be used for storage (by simultaneous exposure with a broadband light beam that reorients the centers) and also for readout. Since by itself it cannot lead to any reorientation, the readout is nondestructive, even at room temperature. The suppressive effect occurs because the M and M A centers reorient only after they have been ionized by the broadband light. The released electron is trapped at an available F center, converting it to an F' center. After this phototransfer process, the ionized M and M A centers can absorb the broadband light and reorient. The long wavelength light suppresses this process by immediately exciting the extra electron out of the F' center, returning it to the ionized center before it has a chance to reorient.

References

5.1 G.H.Brown,W.G.Shaw: Rev. Pure Appl. Chem. It, 2 (1961) 5.2 R.Exelby,R.Grinter: Chem. Rev. 65, 247 (1965) 5.3 J.J.Amodei: Direct Optical Storage Media. In Handbook of Lasers, ed. by R.J.Pressley (Chemical Rubber Co., Cleveland 1971)Chapt. 20 5.4 Z.J.Kiss: IEEE J. Quant. Electron.QE-5, 12 (1969); --Phys. Today 23, 42 (1970)

160 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 5.18 5.19 5.20 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.30 5.31 5.32 5.33 5.34 5.35 5.36 5.37 5.38 5.39 5.40 5.41 5.42 5.43 5.44 5.45 5.46 5.47 5.48 5.49 5.50 5.51 5.52

R. C. Duncan, Jr. and D. L. Staebler B.W. Faughnan, D. L.Staebler, Z.J. Kiss: Inorganic Photochromic Materials. In Applied Solid State Science, Vol. 2, ed. by R.Wolfe (Academic Press, New York 1971) M.Y. Hirshberg: Compt. Rend. 231,903 (1950); Y.Hirshberg, E.Fischer: J. Chem. Soc. (London), Part 1, p. 629 (1953); --J. Chem. Phys. 21, 1619 (1953) T.J.Pearsall: J. Royal Institution I, 77, 267 (1830) P.Curie, M.Curie: C. R. Acad. Sci. (Paris) 129, 823 (1899) K.Przibram: Irradiation Colours and Luminescence, translated and revised by J.E.Caffyn (Pergamon Press, London 1956) E.Ter Meer: Ann. 181, 1(1876) D.Chen, J.D.Zook: Proc. IEEE 63, 1207 (1975) M.Chomat, M.Miller, I.Gregora: Opt. Commun. 4, 243 (1971) P.J.van Heerden: Appl. Opt. 2, 393 (1963) A.N. Carson : U S A F Contract Report, unpublished (1965) E.N.Leilh, A.Kozma, J. Upatnieks, J. Marks, N. Massey: Appl. Opt. 5, 1303 (1966) D.R. Bosomworth, H.J.Gerritson : Appl. Opt. 7, 95 (1968) D.L.Staebler, Z.J.Kiss: Appl. Phys. Lett. 14, 93 (1969) D.L.Staebler, S.E.Sehnatterly, W.Zernik: IEEE J. Quant. Electron. QE-4, 575 (1968) W.Phillips, R.C.Duncan, Jr. : Metallurg. Trans. 2, 769 (1971) D.L.Staebler, S.E.Schnatterly: Phys. Rev. g3, 516 (1971) C.H. Anderson, E.S.Sabisky: Phys. Rev. B3, 527 (1971) R.C.Alig: Phys. Rev. B3, 536 (1971) R.C.Duncan, Jr., B.W.Faughnan, W.Phillips: Appl. Opt. 9, 2236 (1970) R.C. Duncan, Jr.: R C A Rev. 33, 248 (1972) B.W.Faughnan, Z.J.Kiss: Phys. Rev. Lett. 21, 1331 (1968) B.W.Faughnan, Z.J.Kiss: IEEE J. Quant. Electron. QE-5, 17 (1969) J.J. Amodei: Ph.D. Thesis, Univ. of Pennsylvania (1968) B.W.Faughnan: Phys. Rev. B4, 3623 (1971) L.Merker: J. Amer. Ceram. Soc. 45, 366 (1962), also private communication H.C.Kessler, Jr.: J. Phys. Chem. 71, 2736 (1967) D.Huhn, W.Martienssen: Opto-Electron 2, 47 (1970) B.Stadnik, Z.Tronner: Opt. Commun. 6, 199 (1972) R.J.Collier, C.B.Burkhardt, L.H.Lin: Optical Holography (Academic Press, New York 1971) W.J.Tomlinson: Appl. Opt. 14, 2456 (1975) Y.V.Ashcheulov, V.I.Sukhanov: Opt. Spectr. 34, 201 {1973); 34, 324 (1973) W.J.Tomlinson: Appl. Opt. I1, 823 (1972) H. Kogelnik: Bell System. Tech. J. 48, 2909 (1969) K.S.Pennington : Holographic Parameters and Recording Materials. In Handbook ~[ Lasers, ed. by R.J.Pressley (Chemical Rubber Co., Cleveland 1971) Chapt. 21 G.E.Scrivener, M.R.Tubbs: Opt. Commun. 10, 32 (1974) G.E.Scrivener, M. R.Tubbs: Opt. Commun. 6. 242 (1972) A.A.Friesem, J.L.Walker: Appl. Opt. 9, 201 (1970) l.Schneider: Appl. Opt. 6, 2197 (1967) I.Schneider, M.Marrone, M.N.Kabler: Appl. Opt. 9, 1163 (1970) F.Lanzl, U. Roder, W.Waidelich: Appl. Phys. Lett. 18, 56 (1971) F. Lilly : F a Centers in Alkali Halide Crystals. In Physics oJ Color Centers, ed. by W. B. Fowler (Academic Press, New York 1968) Chapt. 3 l.Schneider: Phys. Rev. Lett. 32, 412 (1974) l.Schneider: Appl. Opt. 11, 1426 (1972) U. Roder: Opt. Commun. 6, 270 (1972) H. Blume, T.Bader, F.Liity: Opt. Commun. 12, 147 (1974) l.Schneider, M.Lehman, R.Barker: Appl. Phys. Lett. 25, 77 (1974) J.Burt, H.Knoebel, V.Krone, B. Kirkwood: Appl. Opt. 12, 1213 (1973) D. Casasent, F.Caime: Appl. Opt. 15, 215 (1976)

6. Thermoplastic Hologram Recording J. C. Urbach With 14 Figures

The creation of surface relief holograms by thermoplastic deformation has proven to be an unusually satisfactory recording technique for many types of holography. These holograms, which can be used in either transmission or reflection, are rather pure examples of thin phase holograms, and can be treated accordingly, as described by Kogelnik [6.1]. In this chapter we shall briefly discuss the historical background of the method, describe several of its more important device and process variants, and consider some of the experimental techniques involved in device fabrication and operation. Then we shall discuss both the optical and physical properties important in hologram recording by means of thermoplastic deformation. The former include such characteristics as resolution and bandwidth, sensitivity, diffraction efficiency, nonlinear distortion effects, and noise properties. The latter include cyclic reusability, mechanical durability, and the shelf life of the unused device, the latent image and the completed hologram. It can be said that thermoplastic hologram recording I-6.2] is descended directly from the recording of screened conventional images ("carrier frequency photography") [6.3, 4]. This in turn evolved from the use of thermoplastics for in-vacuo electron beam recording [6.5], which in its turn is a descendant of the Eidophor television system [6.6]. All of these processes have in common the creation of localized electrostatic forces which deform a fluid surface (usually a free surface adjacent to vacuum or gas) into a pattern of surface relief capable of altering the phase of a transmitted or reflected optical readout wave. This phase alteration, if on a scale large compared with the wavelength of the readout light, can be regarded as deflecting that light according to the laws of reflection and refraction. The resulting geometric optics description of the readout process, while simple, is inappropriate for most holographic cases in which the scale of the deformation is often on the order of a few wavelengths. Hence, the more general diffraction theory description [6.1] of readout is normally used.

6.1 Process Description There are two basically different ways of making holograms or holographic spatial filters. One is the photographic approach, in which the hologram is formed by using a photosensitive process to record a naturally occurring

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interference pattern. The other is the synthetic approach, in which a hologram is computed and then created artificially. In the latter approach, it may be possible to create the hologram without the use of any light-sensitive process. This distinction is particularly important when considering thermoplastic holograms, since the direct recording on thermoplastics of patterns created by a scanning, modulated electron beam, already noted [6.5] for historical reasons, can be a powerful tool for the creation of synthetic holograms without the need for optical and photographic intermediate steps. Interest in the electron beam recording process has flourished intermittently since the 1960's at the University of Michigan, and has recently been active at its Environmental Research Institute [6.7]. The different forms of thermoplastic recording technology which are appropriate to these two types of holography all depend, ofcourse, on the use of electrostatic forces to induce plastic flow and thus create the relief pattern which constitutes the phase image or hologram. They differ rather drastically in practical embodiments, and are best described separately. Although most of this chapter will deal with the light-sensitive version used for natural holography, it seems appropriate for both historical and tutorial reasons to begin with a simple description of the electron-beam form of the process.

6.1.! Thermoplastic Electron Beam Recording I f a layer of insulating thermoplastic is deposited on a conductive substrate and placed in a vacuum with the substrate grounded, it can be charged by a scanning electron beam. Such a beam deposits negative charge on the surface of the thermoplastic. Electrical neutrality is maintained by attraction of an equal and opposite positive charge onto the side of the thermoplastic layer in contact with the grounded substrate. The attraction between charges produces a certain electrostatic pressure, which macroscopically is proportional to the square of the surface charge density, and which is exerted on the thermoplastic layer. If the thermoplastic is heated above its softening temperature (a temperature which is actually not very well defined in most such materials), it becomes in principle capable of fluid deformation. In order for deformation to occur, two major conditions must be satisfied. First, the charge density must be nonuniform. Uniform charge, hence uniform electrostatic pressure, will not significantly deform a substantially incompressible fluid such as molten thermoplastic. (An exception to this condition should be noted immediately : If the surface charge density is high enough, the fluid will break up into random deformation patterns, commonly known as "frost" because of their visual appearance. This phenomenon is of considerable significance, and will be discussed subsequently.) Second, the conductivity of the molten thermoplastic must be low enough to permit the fluid flow of deformation to proceed significantly prior to electrical discharge of the thermoplastic. This includes both conductivity normal to and parallel to the surface, since the former collapses the driving field causing electrostatic pressure, while the latter can adversely affect resolution.

Thermoplastic Hologram Recording

163

All deformation of this type occurs in opposition to the force of surface tension, which tends to restore the free surface to the minimum area of its flat state. Continued heating, which maintains the thermoplastic's conductivity at an elevated level, will eventually discharge the surface, and eliminate the forces inducing deformation. Since the thermoplastic remains in the fluid state while heated, the surface tension takes over and restores the surface to its flat state. For this reason, thermoplastic development does not proceed to a steady state deformation pattern, but rather if prolonged or resumed eventually returns the surface to an undeformed state. Thus the process is inherently reversible, sometimes a significant advantage. Linked with this advantage, however, is the need to terminate the development process at or near an optimum state, and by relatively rapid cooling to harden the thermoplastic while it is still deformed, and thus to "fix" the deformation pattern. This need is sometimes a rather difficult one to satisfy properly, and can give rise to more or less severe processing problems. In the actual use of this process for electron beam recording, beam current, dither or focus modulation can be used to modulate the surface charge density and thus the latent electrostatic image. Uniform heating then initiates deformation, and uniform cooling interrupts it to fix the image. Both removable film versions [6.5], using a flexible web substrate, and fixed faceplate versions [6.7, 8] of the process have been operated successfully. Extensive materials work was done at General Electric Co., IBM Corp., and elsewhere to develop thermoplastics compatible with the requirements of vacuum operation and electron beam bombardment. When used in conjunction with high resolution electron optical systems and high optical quality substrates, this form of the process may still turn out to be one of the most suitable means of recording synthetic holograms, either from nonoptical signals, as in synthetic aperture radar, or in the form of computergenerated holograms. When the hologram information is contained in an electrical signal prior to actual hologram recording, some form of direct electron beam recording is often the most desirable way to transform this signal into an optical hologram. In that case, the inherent advantages of thermoplastic electron beam recording over other types of electron beam recording may prove significant. There are also advantages of this form of the process over the photosensitive version discussed subsequently. These include, of course, simplicity of fabrication, absence of a thermoplastic/photoconductor interface with its attendant chemical and electrical problems, and absence of the light absorbing photoconductor which can reduce the efficiency of optical transmission readout.

6.1.2 Photosensitive Recording The remainder of this chapter will be devoted to the photosensitive forms of thermoplastic recording. It is these forms that have seen widespread use in optical hologram recording, and it is these that have been investigated most extensively.

164

.1. c. Urbach

Photoplastic Devices There are two basic versions of the photosensitive devices. The first, shown in Fig. 6.1a, has been termed "photoplastic" by Gaynor and AJtergut [6.3], and is the simpler in terms of structure and process. In this version, the thermoplastic of the electron beam recording process is replaced by a photoconductive thermoplastic. Otherwise, the structure remains unchanged from the elementary form. Now the process steps are as follows: 1) Uniform charging (conductive substrate grounded). 2) Exposure to light. 3) Heating to develop the deformation. 4) Cooling to fix the deformation. 5) Heating, if desired, to erase the deformation. The uniform charging step is generally accomplished by corona charging, but other charging methods, discussed subsequently, are also applicable here. It creates a uniform internal electric field in the material. The exposure step now replaces the former process of electron beam imaging as the means for inducing the nonuniform surface charge density needed for creating a developable latent image. The remaining process steps are the same as in the electron beam recording version. The simplest form o fcharging is of course the use of a corona discharge in air, typically a DC discharge requiring several thousand volts applied to one or more fine wires or an array of small-radius points. The radius of the wires or points must be small enough to assure that local fields exceed those required for air breakdown, so that ionization can occur. The grounded substrate of the device together with the choice of corona potential assures that a relatively weak average electric field exists to move ions of the desired sign toward the device surface. Usually it is necessary to charge that surface to a potential of several hundred volts, corresponding, at typical device thicknesses, to several tens of volts per micron of internal electrical field. For the single-layer form of device, it is sufficient to assure that the surface charge density is uniform. This requirement imposes some restrictions on charging geometry. Either a relatively dense fixed array of wires or points must be used, somewhat larger than the device to reduce edge effects, or a one-dimensional array or single wire must be scanned at a uniform velocity in the orthogonal direction to assure uniform surface charge. Since all theoretical predictions, e.g., Gaynor [6.9-], suggest that the device sensitivity depends at least quadratically on the electric field or charge density, it is clear that uniformity must be good. Estimates of tolerable deviations from uniformity vary widely and are of course dependent on applications, but in general it is advisable to hold these variations under 5 %. The operation of the exposure step is in principle relatively simple. Since the thermoplastic has been made photoconductive, incident light results in the photogeneration of charge carriers throughout the sensitive layer. These are separated by the action of the internal electric field, and, if both holes and electron are mobile, each migrates to the oppositely charged surface, and

Thermoplastic Hologram Recording

165

PHOTOCONDUCTIVE THERMOPLASTIC CONDUCTOR --'~ SUBSTRATE

(a}

CODOCTO f

INSULATING THERMOPLASTIC PHOTOCONDUCTOR

SUBSTRATE

Fig. 6.1a and b. Device cross section (not to scale). (a) "Photoplastic" device configuration: Photoconductive thermoplastic on a conductive substrate. (b) Thermoplastic-overcoated photoconductor device configuration : Nondeformable photoconductor on a conductive substrate

(b)

partially or entirely neutralizes the original charges deposited there during the charging step. If only one sign of charge is mobile, bulk exposure is less effective in neutralizing the surface charge density, but the operating principle is similar. In any case the effect o fexposure-induced reduction in the surface charge density reduces the electrostatic pressure in regions with high exposure relative to that in regions with low exposure. The result is an imagewise variation of electrostatic pressure, hence the developable latent image. Uniformly illuminated areas have uniform surface charge density, so that their latent image are not developable. In terms of spatial frequency response, this means that the process has no spatial DC response, a characteristic requiring special compensation techniques in ordinary photographic use, but naturally suited to offset reference beam holography, matters which will be discussed in a subsequent section. Development is usually carried out by uniform heating as in the electron beam version. Several ways of achieving this heating have been used. These include radiant heating with non-actinic (to prevent immediate photodischarge of the charge pattern) radiation, ohmic heating by passing a current through the conductive substrate coating, ohmic heating by use of RF fields capacitively coupled to the conductive coating and inducing RF alternating currents in it, and heating by means of a hot air stream directed at the thermoplastic surface. In addition to thermal development, use of solvent vapors to soften the thermoplastic is also possible [6.10], although generally more difficult to control than the thermal methods. The rate of development by any of these means can vary from tenths of milliseconds to hours, but is typically on the order of one second in most embodiments of the process [6.47]. The achievement of uniformity in develop-

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ment is rarely easy, and is of course easier in slow thermal development where the device is always close to thermal equilibrium and internal as well as external heat transfer processes have enough time to help reduce heating nonuniformities.

Thermoplastic-Overcoated Photoconductor Devices The other version of the device [6.11] is more complex in structure but has certain advantages that have led to its use in most holographic experiments and applications. It is shown in Fig. 6.lb. It differs from the photoplastic device insofar as the thermoplastic and photoconductor functions have been separated, and are now performed by two different layers, the upper transparent thermoplastic layer having no photoconductivity in this version. Terminology here was somewhat confused by the tendency of certain authors, e.g., Colburn and Dubow [6.12], to use the term "photoplastic" to denote these two-layer devices. For clarity, we use it only in its original meaning of single-layer device. The process steps required for operation of the two-layer devices are slightly more complex. The requirement for this more complex process can be readily, albeit somewhat simplistically and not quite accurately, understood from the following considerations: Exposure and consequent photogeneration in the photoconductor cause opposite charges to migrate to its two interfaces, with the thermoplastic and substrate, respectively. While this reduces the surface potential of the device, it does not reduce the surface charge density, thus creating no imagewise variation of that density on the thermoplastic, hence no developable latent image. This problem is solved by the introduction of another process step, the recharging of the surface to a constant potential. This step deposits additional charges in exposed regions, roughly in proportion to the decrease in surface potential, hence to exposure. Thus the exposure-induced surface potential variation is converted by recharging into a corresponding variation in surface charge density, and therefore into a developable latent electrostatic image. From here on, development, fixing and erasure proceed as in the first version. The requirement for recharging to a constant surface potential can be met by using a screened corona charging device commonly known as a "scorotron" [6.13, 14]. In such a device, a perforated sheet or wire mesh screen is inserted between the corona wires and the device surface and is held at a voltage above (or below) ground approximately equal to the desired surface potential. Flow of ions from the corona to the thermoplastic proceeds through the screen, albeit with slightly reduced efficiency, until the surface potential approaches the screen potential. After the electric field from the screen to thermoplastic approaches zero, further ion flow is to the screen rather than to the thermoplastic. Thus the thermoplastic surface asymptotically approaches the screen potential. Such an arrangement has the additional advantage of holping to assure uniform charging since the potential of the screen itself is uniform because it is made of a highly conductive material. Therefore it forces all areas of the thermoplastic to approach the same uniform potential.

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Although these two advantages generally justify the use of screened coronas, it should be noted that even recharge with an unscreened corona will render the latent image developable. This is presumably a result of preferential deposition of charge in those regions of the surface which are at a lower potential after exposure, leading to the desired exposurewise variation of charge density after recharge. A useful feature of this two-layer version of the device and the corresponding process is that the recharge step largely stabilizes the electrostatic latent image, permitting subsequent exposure to actinic light without significant degradation of the latent image. This occurs for the same reason that recharge is required in the first place: Exposure of the two-layer device alters only the potential, not the surface charge density. Therefore such exposure after the recharge step does not alter the developable latent image, although it does of course affect the undevelopable potential distribution. This holds true only if the thermoplastic is indeed a good insulator, a condition easily satisfied by most thermoplastics. If this exposure is not accompanied or followed by additional charging, it neither erases nor alters the developable latent image. The practical consequence of this is often quite desirable : it permits inspection or even automatic feedback control of the developing image (or hologram) with actinic light. In the case of many panchromatic photoreceptors, all visible light is actinic, hence this feature makes possible inspection or closed loop development control in a manner not possible with the single layer device, or for that matter with most other photographic processes. It should be noted here that the qualitative explanations given thus far for all electrostatic imaging effects, including this last one, are based on a semimacroscopic view. A detailed analysis of the microscopic aspects of the electrostatic fields and pressure distribution does predict a more complex situation. In particular, a weakly developable latent image is formed in the twolayer device even without the recharge step. This prediction has been confirmed experimentally. Likewise, post-recharge exposure does have some effect on the developable latent image. In most practical situations, however, these effects represent a relatively minor correction on those expected from the semimacroscopic view, hence the much simpler qualitative explanation provided by that theory is usually a satisfactory guide for experimental work. Device and Process Variations

As might be expected in a device and process having a number of possible degrees of freedom, many interesting variants have been proposed and tried. We shall omit those that have not, to our knowledge, been used experimentally in the holographic applications of thermoplastic electrophotography. Perhaps the most obvious device variation is the addition of a reflective overcoat to the thermoplastic. This of course greatly increases the efficiency of image reconstruction by reflected light. If the reflective surface layer is so compliant or fragile that it has little effect on the rheological or electrical properties of the

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thermoplastic, and if the exposure of the device is through a transparent substrate, this variant can make possible a significant sensitivity increase, as will be discussed subsequently. Under certain conditions, the reflective layer can also be made conductive, as in the Gamma Ruticons of Sheridon [6.15]. This permits operation of the device in an electroded configuration, eliminating the need for corona charging and resulting in a more convenient process. Another form of device/process configuration which eliminates some of the drawbacks of corona charging has been described by Colburn and Tompkins [6.16]. This uses a transparent charging electrode closely spaced above the thermoplastic layer. A voltage is applied between this electrode and the electrode underlying the photoconductor; this voltage is capacitively divided among the device layers and the gap. When the voltage is high enough to prooduce an electric field in the gap exceeding the breakdown field for air (or other gas) in the gap, a discharge forms across the gap and the thermoplastic surface is charged. This configuration makes possible exceptionally rapid charging of the device. Both this configuration and conventional corona charging have been used in two variants of the process sequence previously described for the thermoplasticovercoated photoconductor device. One is to combine the charging and exposure steps (1 and 2) into a single step of simultaneous charge and exposure. This is usually compatible only with exposure through the substrate if corona charging is used, since most corona charging devices, with their wire discharge and screen arrangements, block exposure from the thermoplastic side. The aforementioned configuration of Colburn and Tompkins [6.16], on the other hand, permits this process variant to function with exposure from either side, and in fact performs better (in terms of resulting diffraction efficiency) if used with this variant. A more radical variant is the combination of Steps 1-3. That is, charging, exposure and development are concurrent, as a result of heating either just prior to or during a combined charge and expose step. This process has been described by various authors [6.10, 17]. It tends to produce especially strong deformations under a given set of conditions, since the charge density continuous to increase in thinner regions as deformation proceeds, thus creating a kind of positive feedback which amplifies the deformation excursion. Some of the strongest deformations reported in [6.173 were obtained by using this type of process.

6.1.3 Process Models and Theories

Unlike many other image recording systems, whose operation involves highly complex chemical processes, thermoplastic deformation imaging is an essentially simple physical process, involving as it does on:y basic electrostatics and fluid flow. It thus promises to be more amenable to detailed theoretical analysis than are most of the other imaging systems. It has been a tempting subject for analyses, many of which were undertaken during the decade from 1963 to 1973.

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Many of the published theories, for example References [-6.18-21] concerned themselves only with the random, or frost, mode of deformation, where there was no initially nonuniform pattern of charge density. A few, e.g., [6.5, 22, 23] did consider the variations in charge density which correspond to image formation. In this section, we shall not discuss these theoretical investigations in detail, but shall note some of their important features. Considerable difficulty is entailed in using the results of these theories as a guide to practical device and process parameters. All of them model the actual experimental situation in a simplified way, while in fact it is often hard to know what model of that situation is actually justified. For example, parameters of importance in the theories, such as surface tension, viscosity, electrical conductivity, and dielectric strength may vary in depth and in time in a manner almost impossible to measure experimentally and difficult to predict theoretically. Even when such a prediction is made, e.g., Mathies et al. [6.21], p. 107, its inclusion would complicate the theory to an unmanageable degree. Thus there still exists no complete and definitive theory of thermoplastic deformation imaging, it now seems that the apparent simplicity of this imaging system was somewhat deceptive. The theoretical results obtained apply to an oversimplified model of the real systems, and have thus far provided only an incomplete guide to process and device optimization. One of the most complete attempts to analyze the imaging system formed by the two-layer class of devices was carried out by Schmidlin in 1967 and is documented in a series of unpublished internal technical memoranda and reports. One of his results [6.24] is given below in condensed form and without derivation only to illustrate their general characteristics. Schmidlin assumed a sinusoidal charge density, created by exposure, at the thermoplastic-photoconductor interface, with the recharge step producing a charge pattern on the top surface of the insulating thermoplastic according to conventional electrostatic theory. He then computed the relative deformation 6D/D, where D is the thermoplastic thickness. His result was: 6D D

K2AEV(e '°t- 1) flfcosh(2nfD)[.q+tanh(2nfD)](49Q-2rtfD)

(6.1)

where t is time, AE is exposure excursion, V is voltage, and Kz is a constant, and where, unfortunately, co, g, [3, 49, and Q are all functions of spatial frequency J~ themselves complicated enough to effectively prevent any sense of a simple relationship between 8D and f. This theory takes into account the possibility of an effective skin tension on the thermoplastic which may differ from the normal surface tension of that material. It also considers the effect of charge leakage during development, and of viscosity. It does assume, as do other theories, that temperature is uniform and constant during development, a generally invalid assumption necessary to avoid further complication in the already complex analysis. The results of the theory,

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plotted numerically, are in qualitative agreement with some experiments, predicting the rather sharply peaked spatial frequency response curve often observed. It does not seem fruitful at this point to develop a more complete theory. Among other things, it would be hard to test experimentally, since, as noted before, it would be extremely difficult to obtain accurate measurements of the key parameters. Theories of Random Deformation

The theories of random deformation were usually intended to provide models for frost imaging, in which relatively high frequency random deformations are modulated by image information. Because of its inherently noisy nature, this mode of imaging is of little or no interest in hologram recording. Nevertheless, since random deformation of this type is the chief source of noise even when it is not being used as an information carrier, it is worthwhile to predict conditions under which such noise can occur. Therefore the theories of frost are of primary interest here as theories of noise in hologram recording. O f the many discussions of frost deformation, perhaps the most extensive is the joint theoretical and experimental report of Matthies et al. [6.21]. The theoretical treatment is based on that of Budd [-6.19] and extends his work to include threshold as well as spatial frequency effects. Earlier treatments of the subject are special cases of this more recent theory. In common with other theories, this one does not treat the problem as a true two-dimensional random deformation, but instead models the real situation by considering the growth of a sinusoidal perturbation of the surface. Both equipotential surface and uniform charge density cases are considered. The underlying physical effects here are that a charged fluid surface tends to increase its surface area as a result of mutual repulsion of the charges, while this increase is opposed by both surface tension and viscous drag. While deformation is under way, the finite conductivity of the fluid tends to discharge it, thus dissipating the charge which drives the deformation. Budd [6.19] predicted that there is a wavelength dependence of the growth rate of the surface perturbation. In general, the wavelengths of most rapid frost growth are well within the range of the most rapid response to images, so that the noise spectrum of the deformation largely overlaps the useful imaging spatial frequency range. Matthies et al. [6.21] show that in all the cases which they consider, including equipotential surface and uniform charge density, and both sequential and simultaneous charging and development, there is a threshold value o f initial surface potential. Below this value frost does not occur at the "dominant", i.e., fastest growing, wavelength predicted by Budd's theory. Such thresholds are in fact observed experimentally, and, under the controlled experimental conditions of [6.21], good agreement was found between theoretically predicted and experimentally observed values of threshold voltages.

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The existence of this threshold is significant in holographic applications insofar as it suggests that there may be conditions under which imaging, i.e., charge-excursion-driven, deformations can grow at a significant rate, while frost deformation cannot develop. This is an area calling for further study, but one which could prove important by permitting dramatic improvements in signal-tonoise ratios. Matthies et al. (Ref. [6.21], p. 93) suggest that in general frost-free deformations will require the use of relatively thin thermoplastic layers, which will run into other limitations arising from finite dielectric breakdown strength. Application and perhaps extension of existing "driven-case" imaging theory could help define these optimum performance regions. One other result of this theory, significant mainly in a negative sense, is a proof that gravitational forces are in fact negligible for thermoplastic layers of interest in holography. Expected on intuitive grounds, this result confirms that the gravitational field can safely be ignored in analysis and experiment (Ref. [6.213, p. 104). 6.1.4 Materials The choice of materials and fabrication procedures for thermoplastic imaging devices is quite broad. The description o f the device structure itself suggests that a wide range ofsubstrates, photoconductors and thermoplastics can in principle be used in such devices. Substrates and Conductive Coatings Considering the device structure one layer at a time, we see that the substrate needs to be transparent and of high optical quality if transmission holography with front exposure is contemplated. If exposure is through the substrate, and optically compensating conjugate image reconstruction is used, requirements on optical homogeneity can of course be relaxed. More generally, it is advisable to select substrate quality according to the usual principle that a hologram is an optical element and that its optical quality must be appropriate to its intended placement in the imaging path. The requirement for transparency can of course be removed if reflected light reconstruction and front exposure are planned, but this is in fact a rare case, since it usually implies such undesirable practices as exposure through a reflective layer, or reconstruction by Fresnel reflection from the thermoplastic surface with a coherent (interfering) image reconstructed after substratc reflection and two-fold transmission, or post-development reflective coating of the finished hologram. It may be most practical if the hologram is to become a master for mechanical replication and thus not used optically. Mechanical requirements on the substrate are generally dictated by the optical ones. Usually, although not always, rigidity is demanded; this requirement can often be relaxed somewhat in the case of transmission holograms. The net consequence of the substrate requirements usually leads to the choice of glass, but occasionally transparent plastics have been used [6.17].

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The optical requirements on the conducting coating used for the ground electrode are similar to those on the substrate itself. Usually they are easy to satisfy because the conductive coating can generally be quite thin, so that its homogeneity is not a problem from the optical standpoint. The electrical requirements may be more stringent, depending on the development mode chosen. I fdirect or RF coupled ohmic heating of this conductive layer is used for development, than it becomes necessary to assure a well-selected (relatively low, typically tens o f ohms per square) and highly uni form resistivity of this layer. I f its only purpose is as an electrostatic ground plane, on the other hand, it is quite adequate if the surface resistance is thousands of ohms per square, and is relatively nonuniform. This is a consequence of the extremely low currents that flow during the relatively slow charging steps, resulting in near-equilibrium operation of this layer. Photoconductors If the device is of the single operational layer (photoplastic) variety [6.3, 25, 26, 46], then some rather special constraints are imposed by the simultaneous requirements of photoconductivity and thermoplastic deformation. Probably the most limited materials range is that required by the photovoltaic version of these single-layer devices, described by Gaynor and Sewell [6.27], but we shall omit discussion of those device here because of their generally low sensitivity. Even the photoconductive version has serious restrictions, because the thermoplastic polymer matrix must support conduction. This has usually been achieved in two ways, either by incorporating a photosensitive dye in the thermoplastic, or by producing a dispersion of photoconductive particles capable of injecting the charge carriers they create into the polymer, which in either case must be capable of transporting these charges. Both these approaches have been used [-6.3, 25] in versions of photoplastic recording. In the former case, the materials used included TCNE-Pyrene and leuco-malachite green with trace malachite green while in the latter, the dispersed photoconductor was either copper phthalocyanine or copper-doped cadmium sulfide in the form of small (generally submicron) particles. The thermoplastic polymer was usually plasticized polystrene of unspecified molecular weight. In addition to the perhaps limited number of possible combinations of sensitizing dyes or particles with suitable thermoplastic matrixes, there is a fundamental tradeoff in the photoplastic devices which has no direct counterpart in two-layer devices. This involves the choice of thickness of the layer. For a given material, one can expect some upper limit to the concentration of photoconductive material, whether it be in dye or particulate form. This limit will probably be imposed by either excessive dark decay or by interference with the desired rheological properties. In practice this has meant that the material must be many microns thick to absorb a reasonably large fraction, say 50%, of the incident light. (Absorption much above 50% is not likely to be desirable if image reconstruction is by transmitted light, since this light will have to pass

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through the same layer, and is likely to be of a wavelength similar to the exposing light.) Typical thicknesses of photoplastic films tend to be in the 20 to 25 tam range [6.25, 26]. Now one will encounter the thickness-imposed resolution or bandwidth limitation of all thermoplastics. The frequency of maximum deformation response and generally the useful spatial frequency bandwidth are inversely proportional to thermoplastic thickness (see pp. 186, 189). If this thickness must be increased to assure more absorption, hence higher photosensitivity, it will be at the expense of bandwith. This is not a linear tradeoffsince absorption is exponential (although actual sensitivity sometimes is not [6.25]), while bandwidth is inversely proportional to thickness. While different quantitatively, this tradeoff is qualitatively somewhat reminiscent of the well-known bandwidth-sensitivity tradeoffs in silver halide emulsions. The consequences of this tradeoff appear to be quite serious in practice, because it prevents attainment of reasonably high sensitivity in the ultrathin (less than 1 gm) layers which both theory and experiment have shown to be the most promising in terms of bandwith and signal-to-noise ratio. The two-layer system has attained favor in holography both because it circumvents this particular tradeoff and because of the greater ease of independently selecting favorable photoconductor and thermoplastic properties. The thickness of the thermoplastic in this case is independent of that of the photoconductor, although macroscopic electrostatic considerations based on capacitive field division suggest that it should be substantially thinner [-6.11]. This means that a thin thermoplastic selected for maximum bandwidth can be used over a photoconductor chosen for maximum light absorption, which property in turn can be achieved by either a high absorption coefficient or considerable thickness. Although there are further constraints and tradeoffs, having to do with development gain and dielectric strength, the extra design freedom of the two-layer device has helped make possible all the published examples of high performance attained by thermoplastics in holographic applications. The other advantage, that of combining almost any photoconductor type with any thermoplastic, has also helped contribute to the superior performance of two-layer devices in holographic applications. This too is not without some restrictions. In particular, the interface between the two must have satisfactory electrical properties. This means that carrier injection from the photoconductor into the thermoplastic must be negligible, as must lateral migration of carriers at the interface. Moreover, when erasability is important, excessively deep trapping sites must not exist at the interface (or in either layer, for that matter) if residual (ghost) image retention is to be avoided. Another restriction on arbitrary pairing of thermoplastic with photoconductor is the one of chemical compatibility, both during fabrication (including solvents involved in the fabrication process) and during the subsequent life of the device. An example of the latter problem might be undesired crystallization of a vitreous photoconductor because of contact with an unsuitable thermoplastic.

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Assuming compatibility has been achieved, there are few restrictions on photoconductor properties other than that of adequate transparency if transmitted light reconstruction is planned. If the sequential mode of process operation is to be used, then the dark decay of the photoconductor must be low enough to assure that random buildup of dark decay charge fluctuations at the thermoplastic-photoconductor interface is an insignificant source of noise. In rapid process cycles, and especially in the simultaneous charge-expose-develop process, dark decay is rarely significant. Other than this, the large range of photoconductor choices has allowed broad experimentation, which has led to considerable success. One of the most widely used photoconductors in two-layer devices is poly-nvinyl carbazole (PVK), sensitized either with Brillant Green dye or with 2, 4, 7 trinitro-9-fluorenone (TNF). The former sensitizer yields lower sensitivity, and has a transmission window in the green region of the spectrum, further reducing its sensitivity there. The latter achieves boths high and nearly pachromatic photosensitivity. The use of TNF, however, requires special precautions against inhalation or ingestion, because this compound has been found to be highly carcinogenic in animal experiments. The proportion of TNF can be increased from relatively low levels up to 1:1 molar, with progessively increasing sensitivity in most instances. The actual composition of the material consists of a solid solution of PVK, free TNF and a PVK-TNF charge transfer complex. The photogeneration efficiency and mobility of electrons and holes in this material are field dependent, but mobility is different for electrons and holes, being higher for the holes, especially when TNF concentrations are low. The theory and practice of dye sensitization of such photoconductors is discussed in detail by Cotburn et al. [6.28] (in their Sects. 3 and 4). That discussion covers problems and techniques of both visible and infrared sensitization. One of the most serious problems observed in the cyclic use of two-layer devices, especially those having PVK photoconductors, is the so-called "ghost image" effect. This effect is the reappearance of a previously erased deformation image after a subsequent charge, recharge and development sequence. Ghost images appear both in the absence of a second exposure and when such an exposure is present, in which case they can be a severe source of background "noise", because their intensity is often close to that of the desired image. Although it is in principle possible that ghost images could arise from trapping effects in the thermoplastic or at the thermoplastic-photoconductor interface, in practice it has been shown that they are normally the result of photoconductor problems. In addition to the indirect theoretical and experimental evidence pointing toward this conclusion, a set of direct experiments conducted several years ago in the Xerox Research Laboratories demonstrated that certainly the thermoplastic itself and probably the interface as well were not involved in the formation of the ghost image. In these experiments, the normal charge-exposerecharge-erase sequence with device and process parameters known to produce ghost images was followed by chemical dissolution of the entire thermoplastic

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layer in a solvent which did not attack the photoconductor. The devices were then recoated with a new layer of thermoplastic. Charging and development then resulted in reappearance of the original image on the surface of the new thermoplastic. In an analysis based on previously published studies of charge generation and mobility, Colburn and Dubow (Ref. [6.12], p. 29 et seq.), conclude that the low electron mobility of PVK/TNF is the primary cause of ghost imaging. A residual exposure-wise pattern of electrons remains behind in the bulk of the photoconductor even after the more mobile holes have been swept through the photoconductor and neutralized at the ground electrode. These relatively immobile electrons are left behind after photodischarge and erasure have largely collapsed the originally strong electric field in the photoconductor. The variation in thermoplastic surface potential caused by the presence of this residual pattern of electrons in the photoconductor results in a corresponding uneven buildup of surface charge density upon the next charging step. It is this buildup that produces the driving force for the ghost image. There are several ways to minimize the ghost image effect. All are based on promoting migration of the residual electrons to the thermoplasticphotoconductor interface, where they can be neutralized by positive ions moving through the thermoplastic to that interface during erasure. At the basic level of material composition, selection of photoconductors to assure comparable hole and electron mobilities can minimize the problem. Of course one must also avoid materials that have deep traps for either sign of carrier. In the particular case of PVK/TNF, Colburn and Dubow [6.12] predicted theoretically and con firmed by experiment that higher TNF concentrations, in addition to increasing absorption and sensitivity, greatly increased electron mobility, resulting in sharply reduced ghost imaging. For example increasing TNF/PVK ratio from 1/10 to 1/4 by weight decreased ghost image effects by as much as an order of magnitude, with the improvement slowly falling off for long erasure times. For a given photoconductor composition, Colburn and Dubow [6.12] suggest several other ways of minimizing the ghost image problem. These include use of longer exposure times for a given total exposure energy and an increased elapsed time between recharge and development. Both these techniques simply allow more time for electrons to be swept to the interface by the residual fields, thus becoming available for later neutralization at that interface. It would also appear that additional delay between development and erasure should have a similar effect. Higher development and erase temperatures can also contribute to effective erasure, because electron (and hole) mobilities increase with temperature. The former methods, of course, are constrained by process and application limitations which may dictate available times for partial and total cycle operation. The latter is often constrained by the danger of thermoplastic or photoconductor degradation at elevated temperatures. Perhaps more satisfactory in practice than these methods is one investigated experimentally by Colburn and Dubow [6.12]. This is the use of a strong (generally white light) flood exposure prior to or during erasure. These authors

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attribute the effectiveness of this method to "increased drift" of the electrons through the bulk of the photoconductor. It might also be the result of massive but spatially uniform photogeneration of holes and electrons in the photoconductor, with a resultant high probability of recombination of some of these holes with most of the ghost electrons, leaving behind a substantially more uniform distribution of electrons in the bulk, while remaining holes are, as usual, swept through the photoconductor to neutralization at the ground electrode. Since uniform surface charge distributions are not developable, the subsequent recharge step does not produce a developable ghost pattern. Whatever the explanation, this method was found to reduce the relative ghost image intensity for given erasure conditions by more than an order of magnitude.

Special Photoconductors Although the great bulk of reported experimental results is based on the use of P V K / T N F photoconductors, a variety of other photoconductors has in fact been used for special purposes. As noted earlier, PVK sensitized with Brillant Green is usable, although typically about an order of magnitude less sensitive than PVK/TNF, and still more subject to ghost images because of low electron mobility in the absence of TNF. A typical concentration of brilliant green is 1 part in 200 by weight relative to the PVK. This gives an absorption peak at 640 nm, closely matched to the 633 nm wavelength of the He-Ne laser [-6.29]. More significant in terms of extending the spectral range beyond the visible is the use of infrared sensitizers. Colburn et al. I-6.30] found that by replacing TNF with 2, 4, 5, 7-tetranitrofluorenone or (2, 4, 7-trinitrofluorenylidene)-malononitrile, sensitivity could be extended as far as the 1.15~tm line of the HeNe laser. Diffraction efficiency was generally on the order of a few percent, and the usual high spatial frequency response was attainable. Sensitivity was approximately 400mJ/cm 2 for 1% diffraction efficiency, far less than in the visible, but still at a usable level. A later advance in infrared sensitization was made by the same authors [-6.28] when they turned to the use of a laser Qswitching dye, Eastman Q-Switch Solution A9740, in conjunction with PVK, giving 1% diffraction efficiency with about 5 mJ/cm 2 and reaching 7% with about 50mJ/cm / exposure, again at 1.15~tm. Although specific data are unavailable, occasional trade press reports suggest that research in the USSR has also led to successful infrared-sensitive photoconductors for thermoplastic recording. In general, it should be expected that devices of this type could be unusually successful in the infrared. Attempts to extend photoconductor sensitivity into the infrared tend to result in more rapid dark decay at or near room temperature because thermal energy begins to be comparable with the available photon energies. In most electrophotographic processes, there is usually a significant delay between charging and exposure and between exposure and development. During these delays, dark discharge competes with the exposure-induced photodischarge, and noise in the dark decay process may become limiting to the

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performance of the system. An unusual advantage of thermoplastic deformation as an electrophotographic development process in this context is the possibility of a very rapid sequence of the key events of charging, exposure, recharging and development. In its ultimate version, simultaneous charging, exposure and development (especially if development is brought about by rapid heating of the thermoplastic from its surface inward to minimize excess dark decay produced by heating the photoconductor) might permit use of in frared sensitive photoconductors otherwise unsuitable for electrophotography. Another direction in which photoconductors have sometimes been pushed is greater sensitivity. Even PVK/TNF is far from being a highly sensitive photoconductor. The author has explored the use of As2Se3, a fast panchromatic chalcogenide photoconductor, in an effort to increase sensitivity [6.31]. This photoconductor is nearly opaque in normal device thickness throughout the visible portion of the spectrum, with some transmission in tile longer wavelength part of the red region. Therefore readout must either be by transmission at extremely low efficiency, or by reflection from the thermoplastic surface, or by a combination of transmission through the thermoplastic, reflection from the thermoplastic-photoconductor interface, and a second transmission through the thermoplastic. In normal reflection readout, the latter two readout effects coexist simultaneously. Because interference among the three succesively diffracted waves obtained in this way can complicate data interpretation, the holograms produced in these experiments were subsequently aluminized to produce pure first surface reflection readout and unambiguous deformation measurement. Using this method, it was found that sensitivities were at least two orders of magnitude greater than those obtained with PVK/TNF. O f this increase about one order of magnitude is attributable to the more sensitive photoconductor, the rest to the readout method (see pp. 193, 196). As with infrared-sensitive photoconductors, this high sensitivity material has relatively high dark decay and benefits from a rapid sequential or simultaneous type of process. The use of this type of photoconductor has thus far been only exploratory, but its ability to achieve these sensitivities at a normal (400 cyc./ mm) spatial frequency promises unusually high informational sensitivity, which ill some uses may offset the more difficult readout requirements.

Thermoplastic Materials The essential requirement for any thermoplastic is the ability to retain charge as it passes through its glass transition temperature and becomes soft enough for reasonably rapid deformation. I f the device is to be used repeatedly, of course, this basic requirement must be supplemented by an ability to retain its electrical and rheological properties through many successive cycles of reuse. Many thermoplastics have been investigated for use in electron beam recording devices as well as in both single- and two-layer photosensitive devices, Thermoplastic-like materials of the type useful in information recording have all been organic polymers. In principle they could be either an amorphous or a

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crystalline type of polymer. The crystalline type has the potential advantage of a sharply defined melting temperature, which might make process control easier to achieve. Crystalline thermoplastics generally consist of many small crystals embedded in an amorphous matrix having a somewhat different refractive index. Consequently substantial light scattering occurs in such polymers, rendering them cloudy and entirely useless for transmitted light readout. Although they might be of some use in the type of reflected light readout appropriate to opaque photoconductors such as those noted in the preceding section, they have in practice been neglected because almost all investigations have concentrated on transmitted light readout. The amorphous polymers which have universally been used in thermoplastic recording change from a substantially solid phase (in which deformation, if it occurs at all, is of the elastic type) to a substantially fluid (generally nonNewtonian) state over a finite range of temperatures. The change is known as the glass transition, and the midpoint of the temperature range over which it occurs is called the glass transition temperature, usually denoted Tg. In general, this range tends to be narrower if the polymer has a narrow distribution o f molecular weights, or if the average molecular weight is low. The value of Tg and the width of the transitional range do not appear to correlate in any simple way with the suitablity of a polymer for thermoplastic recording. However, for image retention it is necessary to be sure that Tg and the transition width are so chosen that the lower end of the plastic flow range is well above room temperature;if any significant amount of"creep" is possible, gradual erasure of the deformation pattern will occur under the influence of surface tension. It should be noted here that elastic deformation of the polymers ordinarily used for thermoplastic imaging is entirely negligible, so that no measurable deformation ordinarily occurs in the absence of the heating step. On the other hand, a deliberate choice of polymers capable of extraordinarily high elastic deformation and having substantially no fluid flow at room temperature has made possible a different type o fcyclic imaging device, the Ruticon, described by Sheridon [6.15], operating entirely on the principle of elastic rather than flow deformation. In this section we shall not attempt a detailed description of the selection, design or synthesis of thermoplastics especially suited for deformation recording, but shall survey some of the salient features of this aspect of the technology. Many different polymers have been tried with varying degrees of success since the early research on thermoplastic electron beam recording. Polystyrene of various molecular weights was an early and moderately successful material in the former application. Polystyrene was also used with suspended or dissolved photoconductors in single-layer photosensitive devices [6.9, 26]. Although polystyrene has also been used in two-layer photosensitive devices [6.32], much of the early work on both frost mode image recording and on holographic recording was done with Staybelite Ester 10 (available from Hercules, Inc., Wilmington, Del.). This material, a derivative of a natural tree resin, has never been fully characterized. Although it has excellent resistivity and can lead to high

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deformation holograms, Staybelite has poor cycling properties, usually being limited to the range of 10 to 100 cycles before its properties degrade significantly. It can be recommended for the casual experimenter or for low recycling applications because of its ready availability and ease of preparation. However, because of its natural origin and uncharacterized structure, significant batch-tobatch variations can occur, sometimes frustrating orderly experimental progress. Another thermoplastic which gives comparable, but generally more consistent results is Piccopale H-2 I-6.29] (available from Pennsylvania Industrial Chemicals Corp., Clairton, Pa.). Some significant advances in thermoplastic materials were made in the course of work aimed primarily at electron beam recording. The research of Anderson et al. [6.33] was intended to develop materials capable of repeated cycling in that mode of operation. Although some of the work reported by these authors was done in order to minimize the deleterious effects of outgassing and radiation damage unique to electron beam recording in a vacuum, many of their experiments were carried out with corona charging in air, and some of their main concepts are transferable to cyclic devices of the photosensitive type. In particular, they emphasize the need for using a nonvolatile plasticizer to avoid hardening of the polymer (and consequent change of Tg and development requirements) with time and repeated heating cycles. They also proposed a key principle for long-term cycling by balancing the two opposing effects that usually degrade a polymer subjected to radiation (or, in our case, the similar damaging effects of heating, ozone and ion bombardment). These effects are, first, cross linking of polymer chains which tend to harden the material, increasing viscosity and Tg; and second, scission of polymer chains, which tends to lower viscosity and Tg. Obviously it is best to minimize both these effects, but because they cannot be entirely eliminated, the optimum design of polymers requires that the two effects both occur to an equal and therefore offsetting degree. Such self-compensating polymers can have remarkably good cycling characteristics. Because the two effects may have different types of dependence on the degrading in fluences, it is clear that optimization of a thermoplastic may need to be specific to a particular set of process parameters. Thus it has always been necessary to test thermoplastics under more or less realistic use conditions to assure that this design principle is effectively utilized. Anderson et al. [6.33] explored a variety ofstyrene-methacrylatecopolymers, compensating the cross-linking tendencies of the styrene with the scission characteristics of the methacrylates. Of the many different methacrylates tried, particularly good results were obtained with octyl-decyl methacrylates. The best cycling results reported in [6.33] under electron beam recording conditions were 50000 cycles using a copolymer of 85 % styrene with 15 % octyldecyl methacrylate. No significant changes in required process parameters (charging current density, development temperature, development time) and deformation were observed during this test sequence. The same investigators (Ref. [6.33], p. 149) extended their tests to single-layer photoconductive devices, adding n-vinyl carbazole to the copolymers used for

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electron beam recording. Partial success was reported, with a moderate increase in development and erase temperatures during 11 500 cycles. It appears simpler, as well as more effective in terms of recording properties, to use the copolymers in two-layer devices, for the reasons of relatively independent constituent optimization noted previously. This was done by several workers [6.12, 16] with considerable success. For example, Colburn and Tompkins [6.16] reported the use in two-layer devices of the styrene-octyl-decyl-methacrylate copolymer (which they refer to as a terpolymer in their paper), with a mole ratio of 85 %, 9 %, and 6 % for the respective constituents. Used with a corona discharge in air, this material showed little degradation for about 100 cycles, then degraded slowly in holographic performance to about 1000 cycles, and finally fell offrapidly above 1000 cycles. Little change in Tgoccurred throughout a 5000 cycle test. When used with the parallel plane charging apparatus mentioned previously, performance degraded very rapidly, becoming unacceptable in 30 to 40 cycles. Attributing this degradation to ozone attack on the thermoplastic in the confined charging structure, Colburn and Tompkins [6.16] replaced air with argon gas in a sealedcell version of this apparatus, and found substantially stable holographic performance for 5000 cycles, although in this case a moderate increase in T~ was observed. The latter fact is further confirmation of our earlier remark regarding the need to optimize polymer formulation for a given set of process conditions. Once ozone degradation is eliminated as a major cause of thermoplastic deterioration, the main remaining source of degradation in parallel plane charging devices appears to be sputtering of the thermoplastic in the high fields characteristic of this configuration. Such sputtering removes material in a random manner from the thermoplastic surface, resulting in a roughened surface, whose light scattering degrades signal-to-noise ratio. Further sputtering can remove so much material that diffraction efficiency also is degraded. The lower fields typical of corona charging in air should substantially reduce the amount of sputtering to be expected. Colburn and Tompkins [6.16] nonetheless reported some surface damage to thermoplastics in this mode of use as well. An alternative to operation in an atmosphere of an appropriate inert gas is the development of an ozone-resistant thermoplastic. One such material reported in [6.16] is a vinyl-toluene copolymer of unspecified constituent proportions. Although incapable of achieving diffraction e fficiencies in excess of 1%, this material, operated so as to give efficiencies of a few tenths of a percent, was able to cycle well over 5000 times using corona charging in air, thus demonstrating a very high resistance to ozone attack. Although it had a high and stable signal-to-noise ratio, this thermoplastic showed poor response to spatial frequencies above 500 cyc./mm (Ref. I [6.12], p. 54). The combination of low diffraction efficiency and limited spatial frequency response may often prove to be an excessive price for good cycling in air. A hydrogenated version of this vinyl-toluene thermoplastic was reported by Colburn and Dubow [6.12]. This material gave diffraction efficiencies as high as 2%, but its efficiency was unstable, rising by over an order of magnitude from start to about 1000 cycles, then falling rapidly.

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Still another thermoplastic discussed in [6.12] is a "highly stabilized ester resin". Whether this is a refined or improved version of the Staybelite Ester 10 mentioned earlier is unclear from the description given in that report. This material, like the styrene-methacrylate type, showed fairly rapid decline of diffraction efficiency when corona charging is used in air, but had constant response up to 3000 cycles in an argon-filled parallel plane charging device. However, its softening temperature rose significantly more during those 3000 cycles. This rise in Tg is also shared by the two vinyl-toluene materials. Another thermoplastic used with considerable success [6.34] is Foral 105 (from Hercules, Inc.). Overall, the styrene-methacrylate materials developed by Anderson et al. [6.33] still appear to be the best choices for most applications of thermoplastic hologram recording. Capable of several thousand cycles with minor degradation when protected from ozone, they enhance process stability while retaining the traditional thermoplastic virtues of high spatial frequency response and diffraction efficiency. Even the advanced work on thermoplastics, noted above, has not given us a deformable material free from all problems. Further optimization of these materials in the context of specific devices and applications will be needed if better cyclic performance is required.

6.1.5 Fabrication Techniques Thus far we have discussed the materials themselves without discussing their actual fabrication into working devices. While it is not the intent of this section to provide a detailed instruction manual on the fabrication of these devices, some major aspects of fabrication will be considered here. This is appropriate because of the crucial role of fabrication techniques in the making of any complex optoelectronic device, above all if that device must perform the multiple functions of thermoplastic imaging repeatably and uniformly.

Substrates and Conductive Coatings The substrate which forms the foundation for these devices need not be further discussed here. Suitable substrates, either glass or plastic, are generally obtainable commercially, and are no different from any other optical recording medium substrate. Although glass has been the most widely used substrate material, mylar, cronar, and other plastics have also been used with excellent results [see, e.g., Ref. [6.17], p. 210). Likewise, fabrication of the conductive layer poses few special problems. Several commercially coated glass substrates are available, for example, indium oxide coated glass from Pittsburgh Plate Glass Co. In addition to these, many others have been custom fabricated. Thin conductive layers of metal have been coated by evaporation on plastic or glass, with just enough thickness to achieve electrical continuity while still remaining sufficiently transparent for satisfactory

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transmitted light reconstruction. Metals used include aluminum, gold, chromium-gold alloys, and silver. Of these, chromium-gold is probably most satisfactory. Conductive compounds often give better results when low resistivity is desired. Aside from the indium oxide already mentioned, satisfactory coatings have been made from tin oxide and antimony oxide, or mixtures of these oxides. Coating techniques for these materials often involve evaporation or reactive sputtering of these materials in an oxygen atmosphere, or in moist air. Some conductive coating fabrication techniques which require oxidation reactions upon contact of a liquid with a hot glass substrate in air result in severe residual stresses of the suddenly cooled glass, which distort it and produce substantial stress birefringence. Since, as noted above, a hologram must be regarded as an optical element, it is evident that substrates with these optical defects are not usable in certain applications. It has already been stated that the resistivity of conductive coatings used for direct ohmic heating should generally be in the range of 10 to 100 ohms per square. If uniform development is required, the resistivity must be controlled rather tightly. It has been suggested (Ref. [6.35], p. 110) that the extreme sensitivity of development rates to thermal power input requires that resistivity be kept uniform to within 1 or 2 percent. This degree of uniformity cannot be obtained from any commercial coatings. The authors of [6.35] found that custom reprocessing of commercially available conductive substrates was required to achieve satisfactory uniformity in resistivity. Photoconductor Fabrication

Fabrication of the photoconductive coating falls into two radically different categories. The rare examples of devices utilizing a vitreous photoconductor such as As2Se 3 require vacuum evaporation of the photoconductor onto a (typically) glass substrate. Because such devices have, to our knowledge, only been used for hologram recording in a few experiments, further discussion of this rather difficult coating technique does not seem warranted here. We shall therefore restrict this section to the fabrication techniques for organic photoconductors and specifically for the various forms of poly-n-vinyl-carbazole (PVK) almost universally used in the two-layer devices of most interest here. The object of photoconductor coating is of course to produce uniform optical, electrical and thermal properties. This requires that the material being coated be homogeneous and that the coating thickness be uniform. While quantitative tolerances on these parameters have never been definitely determined, it is clear that serious response variation within a sample, or among samples, can follow from such photoconductor variations, because they will affect field strengths within and field division between the photoconductor and the thermoplastic, hence local device sensitivity. They can also affect sensitivity by way of altering light absorption. Thickness or thermal conductivity variation can also affect the uniformity of development, because the photoconductor is in the path of heat conduction to the thermoplastic if ohmic heating is used, and in

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the path of heat conduction from the thermoplastic if direct surface heating is used. Coating of PVK has generally been done from a solution. The various techniques of coating all have thickness uniformity as their object, hence are naturally unable to compensate in any way for solution inhomogeneities. It is not particularly easy to obtain entirely uniform solutions of PVK/Brillant Green or PVK/TNF. Various procedures have been described in the literature. For example, the solid PVK and T N F in the desired proportions were dissolved in a 1:1 mixture of 1, 4 dioxane and dichloromethane to obtain about a 6% concentration of solute [6.17]. This solvent requires coating in a relatively dry (less than 25 % relative humidity) atmosphere to avoid fogging of the coating which can result when the cooling of the photoconductor by rapid evaporation of the solvent causes condensation of atmospheric moisture on the surface. Other solvents which create a less severe fogging problem include 1, 1,2trichloroethane and tetrahydrofuron. A relatively detailed prescription for effective use of the latter is given in (Ref. [6.3.5], p. 111). PVK is first dissolved in the proportion of 67 grams per liter of this solvent. This mixture is stirred for 8 to 12 h to ensure complete dissolution of the PVK. It is then filtered, and the desired amount of TNF is added, followed by another four hours of stirring. Although not explicitly mentioned in this prescription, a second filtering after adding the T N F would seem to be desirable. Because of solvent loss during mixing, additional tetrahydrofuran is added back to restore proportions to the desired level for subsequent coating. It is noted in [6.353 that even this relatively elaborate procedure does not assure complete homogeneity of the photoconductor coatings, which remain subject to small defects attributable to the solution rather than the coating procedure. This procedure itself can take several forms. Dip coating, or the equivalent method of drain coating, results in deposition of a thin layer of solution on the substrate as it is being withdrawn vertically from the free surface of the solution. Various forms of doctor-blade or roller coatings have also been used, with positive mechanical control of coating thickness. Spin coating is a highly developed technique in other fields (such as photoresist coating) which could be adapted to this operation. Thus far, however, dip coating remains the most common technique, and, when properly carried out, can give highly uniform results. In dip coating, the thickness is determined primarily by the density, viscosity, surface tension and vapor pressure of the solution and by the rate of withdrawal of the substrate from it. The solution (which of course must be able to wet the substrate) tends to run back into the container from the substrate surface. If the solvent is sufficiently volatile, its loss raises the viscosity of the coated surface to the point where further draining back of the coating into the solution tank no longer occurs, and the coating thickness is stabilized. Over some range of withdrawal speeds, the coating thickness increases with this speed. This range is usually in the low tens of cm per min, (for example, 5 to 24 cm/min for the solution described in [6.35] and summarized above) but depends on the solvent

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and viscosity selected. In practice, control of thickness in the coating is usually obtained by selecting solute concentration to adjust viscosity, and then adjusting withdrawal speed to obtain the exact thickness desired. Uniformity of the coating requires careful construction and control of the apparatus. Naturally, withdrawal must be smooth in order to avoid local variations in instantaneous velocity, which would result in corresponding variation in coating thickness. Likewise, vibration must be carefully avoided because it can easily result in agitation of the free surface of the solution, again producing localized variations in instantaneous withdrawal speed. Excessively high solvent vapor pressure, in addition to producing fogged ("blushed") coatings in high relative humidity ambients, can also result in significant variation of local viscosity near the solution surface during the course of a coating. This produces a taper in coating thickness, which can prove objectionable when using large substrates and low withdrawal speeds. In principle, this effect could be compensated by using a variable withdrawal speed, but in practice this has generally not proven necessary if reasonable choices of solvents were made. Despite all the difficulties of obtaining high quality dip coatings, the method has generally been more satisfactory than doctor-blade coating, perhaps since the former depends on the choice of macroscopic parameters rather than on mechanical precision to assure uniformity. Once the photoconductor coating has been applied, it must be cured by careful drying at an appropriate temperature and in a contamination-free ambient. I f there are no problems o f solvent incompatibility, complete drying of the photoconductor may not be required prior to the next stage of thermoplastic coating, since the PVK solvent can usually diffuse and evaporate through the thermoplastic layer.

Thermoplastic Fabrication The same choices of coating techniques are available for thermoplastics as for organic photoconductors. Once again, dip coating has generally been the preferred method in experimental practice. There is of course an additional constraint on the thermoplastic solvent, namely, that it not attack or otherwise undesirably interact with the underlying photoconductor coating. For each thermoplastic used with a given photoconductor, it has generally been possible to find a solvent which meets this requirement. The particular solvents used also depend on the thermoplastic. If the photoconductor is PVK/TNF and Staybelite Ester 10 is used as the thermoplastic, suitable solvents include petroleum ether and hexane, and typical thermoplastic concentrations are around 20% solid. If the same photoconductor is to be used with styrene/methacrylate copolymers, the latter can be dissolved in naphtha, typically at fairly similar concentrations, around 20 % to 25 %. If the thermoplastic chosen is Piccopole H-2, a suitable solvent is iso-octanes, with solid again at similar concentrations.

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After coating to the desired thickness, the relatively low volatility thermoplastic solvent must be removed, usually by oven baking at temperatures in the range of 50 "C to 75 °C for times of one to several hours. The typical completed device will have a thermoplastic thickness in the range of 0.2 to 2 ~tm. Macroscopic capacitance arguments suggest that a high ratio of photoconductor to thermoplastic thickness will lead to higher fields across the thermoplastic, hence higher sensitivity when all else is equal. Analysis of microscopic driving forces at high spatial frequencies predicts rapid (exponential) fail-off of high spatial frequency response with thermoplastic thickness. Both of these factors, together with the near-reciprocal dependence of the frequency response peak location and width upon thermoplastic thickness, have resulted in an emphasis on thin thermoplastic coatings, with the result that coatings over 1 lam in thickness are not widely used, and most devices are made with thermoplastic coatings in the vicinity of 0.5 [am.

Overcoating and Matrixing The fabrication techniques described thus far are all that are needed in making conventional two-layer devices. If reflective or conductive metallic overcoatings are desired, vapor deposition in vacuum of metallic indium or gold-indium alloys can provide such coatings. These must generally be quite thin, usually under a few tens of nanometers in average thickness, if their mechanical stiffness is not to inhibit deformation of the thermoplastic, reducing absolute response and moving the peak of the frequency response curve toward lower spatial frequencies. The overcoating must also not inject charge into the thermoplastic, and must not provide nucleation sites for the initiation of random frost deformations. 1f a reflective coating is intended to serve as an electrode in order to permit direct electrical charging of the device, it must have enough integrity to maintain electrical continuity. If in addition the device is to be reused, then the overcoat must not break up or agglomerate during the perturbation of development and erase cycles. This last requirement has never been adequately satisfied in practice ; hence overcoated reflective devices can rarely exceed a few, if any, cycles of reuse. Post-deformation metallization of devices not intended for reuse is a much simpler matter, and can be done by vapor deposition of metals such as aluminum, silver or gold in relatively arbitrary thicknesses. The main concern here is to avoid heating of the thermoplastic above T~ by radiation from the evaporation source. Substrate cooling is often required to prevent erasure of the developed image when metallizing thermoplastic holograms in this way for high efficiency reflective readout. The most elaborate types of device fabrication attempted to date are those aimed at matrix-addressed control of ohmic development of individual small holograms in an array of holograms intended for use in an optical memory. Following the first description of such an array by Lin and Beauchamp [6.36], extensive further work was done at RCA and Harris. A description of the

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required array fabrication techniques is given in Appendix B (p. 84) of Colburn and Dubow [6.12]. Because of the previously noted sensitivity of device performance to development parameters, considerable care must be taken in the fabrication of such addressing arrays to assure uniform performance in all locations. Whether this type of array fabrication can become a practical process for large-scale production is still uncertain.

6.2 Holographic Properties 6.2.1 Bandwidth and Resolution The theoretically expected bandpass response of thermoplastic imaging devices has been observed in ahnost all experiments. Because of the difficulty of accurately modeling the complete experimental situation, close agreement between theory and experiment has never been observed. Therefore we remain with a semi-empirical description of the dependence of spatial frequency response upon the main device and operating parameters. The most important of these parameters is thermoplastic thickness. The frequency Vp of the peak of the frequency response depends more or less inversely upon the thickness D of the thermoplastic. A typical empirical relationship is

l/3D~Vp< 1/2D with the value of Vp increasing more or less logarithmically with voltage for a given thickness. The bandwidth of usable frequency response around this peak is quite variable, depending upon material properties, voltage (field strength) and manner of development. Under some circumstances, relatively broad peaks in frequency response are observed, with resultant high usable bandwidths. With other modes o f operation, the peaks are sharper, and the bandwidth much lower. Since, for low deformations, the diffraction efficiency depends quadratically upon the deformation, it is often reasonable to define the bandwidth in deformation response as the bandwidth measured to the spatial frequency values at which deformation has fallen to 1/]/~ of its peak value, which corresponds to diffraction efficiency al 50 % of its peak value. For some applications, however, especially those involving Fourier holograms, a more uniform frequency dependence of diffraction efficiency is required, resulting in a smaller usable bandwidth. Using the foregoing definition of bandwidth, values of the full bandwidth (note that the frequency response curve is generally not symmetric about its peak) have been found to range from as much as 3/4D to as little as 1/6D. The higher values have been observed in our laboratories under rather atypical process conditions, including very slow development taking minutes rather than

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4-

== o=3. v

,,=uJ 2-

7,

Fig. 6.2. Spatial frequency response of thermoplastic-overcoated photoconductor device, thermoplastic thickness 1.1 /am, beam ratio 1 : 1 (from Urbach and Meier [6.38]) 100

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SPATIAL FREQUENCY (cy/mm)

tens or hundreds of milliseconds. Even more atypical results have occasionally been observed. One of these is a double-peaked frequency response, with a peak at very low spatial frequencies, and another near the 1/2D frequency. This result is sometimes time dependent in the following way: the low frequency peak occurs early in a relatively slow development process, then erases as the high frequency peak appears with further development. Under some circumstances, not fully understood, the low frequency peak does not erase entirely before the high frequency one develops, resulting in the retention of the double peak in the final recording as reported by Lee [6.373. Lo et al. [6.323 have reported similar results, noting that the low frequency peak was observed at relatively low surface charge densities. Figures 6.2 through 6.5 show some fairly representative spatial frequency response curves reported in the literature. These should make it abundantly clear thai there is no such thing as a single frequency response curve. Moreover, since these curves are always dependent on development time and temperature, even setting the basic process parameters of thermoplastic thickness and voltage does not uniquely determine the frequency response of the device. Figure 6.4 illustrates this by showing, for the aforementioned slow development and high bandwidth process, how the frequency response curve evolves with development time, with its peak moving to higher spatial frequencies as development proceeds. All of the foregoing remarks apply specifically to the sequential process mode. The highest spatial frequency response in this mode was reported by

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15f

v--